How many four letter distinct initials can be formed using the alphabets of English language such that the last of the four words is always a consonant?
How many four letter distinct initials can be formed using the alphabets of English language such that the last of the four words is always a consonant?
A question paper has two parts, A and B, each containing 10 questions. If a student has to choose 8 from part A and 5 from part B, in how many ways can he choose the questions?
A question paper has two parts, A and B, each containing 10 questions. If a student has to choose 8 from part A and 5 from part B, in how many ways can he choose the questions?
a,b,c,d and e are five natural numbers. Find the number of ordered sets (a,b,c,d,e) possible such that a+b+c+d+e=64.
a,b,c,d and e are five natural numbers. Find the number of ordered sets (a,b,c,d,e) possible such that a+b+c+d+e=64.
In a railway compartment, there are 2 rows of seats facing each other with accommodation for 5 in each, 4 wish to sit facing forward and 3 facing towards the rear while 3 others are indifferent. In how many ways can the 10 passengers be seated?
In a railway compartment, there are 2 rows of seats facing each other with accommodation for 5 in each, 4 wish to sit facing forward and 3 facing towards the rear while 3 others are indifferent. In how many ways can the 10 passengers be seated?
A question paper consists of three sections 4,5 and 6 questions respectively. Attempting one question from each section is compulsory but a candidate need not attempt all the questions. In how many ways can a candidate attempt the questions?
A question paper consists of three sections 4,5 and 6 questions respectively. Attempting one question from each section is compulsory but a candidate need not attempt all the questions. In how many ways can a candidate attempt the questions?
What is the value of 1 *1! +2 *2!+3 *3! + .............. n *n!
where n! means n factorial or n(n-1)(n-2) ............1.
What is the value of 1 *1! +2 *2!+3 *3! + .............. n *n!
where n! means n factorial or n(n-1)(n-2) ............1.
A two member committee comprising of one male and one female member is to be constitute out of five males and three females. Amongst the females. Ms. A refuses to be a member of the committee in which Mr. B is taken as the member. In how many different ways can the committee be constituted ?
A two member committee comprising of one male and one female member is to be constitute out of five males and three females. Amongst the females. Ms. A refuses to be a member of the committee in which Mr. B is taken as the member. In how many different ways can the committee be constituted ?
In how many ways can 5 different toys be packed in 3 identical boxes such that no box is empty, if any of the boxes may hold all of the toys?
In how many ways can 5 different toys be packed in 3 identical boxes such that no box is empty, if any of the boxes may hold all of the toys?
There are three prizes to be distributed among five students. If no students gets more than one prize, then this can be done in:
There are three prizes to be distributed among five students. If no students gets more than one prize, then this can be done in:
How many ways can 10 letters be posted in 5 post boxes, if each of the post boxes can take more than 10 letters?
How many ways can 10 letters be posted in 5 post boxes, if each of the post boxes can take more than 10 letters?
12 chairs are arranged in a row and are numbered 1 to 12. 4 men have to be seated in these chairs so that the chairs numbered 1 to 8 should be occupied and no two men occupy adjacent chairs. Find the number of ways the task can be done.
12 chairs are arranged in a row and are numbered 1 to 12. 4 men have to be seated in these chairs so that the chairs numbered 1 to 8 should be occupied and no two men occupy adjacent chairs. Find the number of ways the task can be done.
Three gentlemen and three ladies are candidates for two vacancies. A voter has to vote for two candidates. In how many ways can one cast his vote?
Three gentlemen and three ladies are candidates for two vacancies. A voter has to vote for two candidates. In how many ways can one cast his vote?
When six fair coins are tossed simultaneously, in how many of the outcomes will at most three of the coins turn up as heads?
When six fair coins are tossed simultaneously, in how many of the outcomes will at most three of the coins turn up as heads?
If the letters of the word CHASM are rearranged to form 5 letter words such that none of the word repeat and the results arranged in ascending order as in a dictionary what is the rank of the word CHASM?
If the letters of the word CHASM are rearranged to form 5 letter words such that none of the word repeat and the results arranged in ascending order as in a dictionary what is the rank of the word CHASM?
The letter of the word LABOUR are permuted in all possible ways and the words thus formed are arranged as in a dictionary. What is the rank of the word LABOUR?
The letter of the word LABOUR are permuted in all possible ways and the words thus formed are arranged as in a dictionary. What is the rank of the word LABOUR?
There are five women and six men in a group. From this group a committee of 4 is to be chosen. How many different ways can a committee be formed that contain three women and one man?
There are five women and six men in a group. From this group a committee of 4 is to be chosen. How many different ways can a committee be formed that contain three women and one man?
How many words of 4 consonants and 3 vowels can be made from 12 consonants and 4 vowels, if all the letters are different?
How many words of 4 consonants and 3 vowels can be made from 12 consonants and 4 vowels, if all the letters are different?
In how many ways can 15 people be seated around two round tables with seating capacities of 7 and 8 people?
In how many ways can 15 people be seated around two round tables with seating capacities of 7 and 8 people?
A box contains 10 balls out of which 3 are red and rest are blue. In how many ways can a random sample of 6 balls be drawn from the bag so that at the most 2 red balls are included in the sample and no sample has all the 6 balls of the same colour?
A box contains 10 balls out of which 3 are red and rest are blue. In how many ways can a random sample of 6 balls be drawn from the bag so that at the most 2 red balls are included in the sample and no sample has all the 6 balls of the same colour?
Find the number of ways in which 8064 can be resolved as the product of two factors?
Find the number of ways in which 8064 can be resolved as the product of two factors?
If 6Pr = 360 and If 6Cr = 15, find r ?
If 6Pr = 360 and If 6Cr = 15, find r ?
In how many ways 4 boys and 3 girls can be seated in a row so that they are alternate.
In how many ways 4 boys and 3 girls can be seated in a row so that they are alternate.
A class photograph has to be taken. The front row consists of 6 girls who are sitting. 20 boys are standing behind. The two corner positions are reserved for the 2 tallest boys. In how many ways can the students be arranged?
A class photograph has to be taken. The front row consists of 6 girls who are sitting. 20 boys are standing behind. The two corner positions are reserved for the 2 tallest boys. In how many ways can the students be arranged?
Goldenrod and No Hope are in a horse race with 6 contestants. How many different arrangements of finishes are there if No Hope always finishes before Goldenrod and if all of the horses finish the race?
Goldenrod and No Hope are in a horse race with 6 contestants. How many different arrangements of finishes are there if No Hope always finishes before Goldenrod and if all of the horses finish the race?
How many number of times will the digit 7 be written when listing the integers from 1 to 1000?
How many number of times will the digit 7 be written when listing the integers from 1 to 1000?
From 6 men and 4 ladies, a committee of 5 is to be formed. In how many ways can this be done, if the committee is to include at least one lady?
From 6 men and 4 ladies, a committee of 5 is to be formed. In how many ways can this be done, if the committee is to include at least one lady?
In an examination paper, there are two groups each containing 4 questions. A candidate is required to attempt 5 questions but not more than 3 questions from any group. In how many ways can 5 questions be selected?
In an examination paper, there are two groups each containing 4 questions. A candidate is required to attempt 5 questions but not more than 3 questions from any group. In how many ways can 5 questions be selected?
How many Permutations of the letters of the word APPLE are there?
How many Permutations of the letters of the word APPLE are there?
There are 6 equally spaced points A,B,C,D,E and F marked on a circle with radius R. How many convex pentagons of distinctly different areas can be drawn using these points as vertices?
There are 6 equally spaced points A,B,C,D,E and F marked on a circle with radius R. How many convex pentagons of distinctly different areas can be drawn using these points as vertices?
In how many ways can seven friends be seated in a row having 35 seats, such that no two friends occupy adjacent seats?
In how many ways can seven friends be seated in a row having 35 seats, such that no two friends occupy adjacent seats?
In how many ways can the letters of the word EDUCATION be rearranged so that the relative position of the vowels and consonants remain the same as in the word EDUCATION?
In how many ways can the letters of the word EDUCATION be rearranged so that the relative position of the vowels and consonants remain the same as in the word EDUCATION?
A selection committee is to be chosen consisting of 5 ex-technicians. Now there are 12 representatives from four zones. It has further been decided that if Mr. X is selected, Y and Z will not be selected and vice-versa. In how many ways it can be done?
A selection committee is to be chosen consisting of 5 ex-technicians. Now there are 12 representatives from four zones. It has further been decided that if Mr. X is selected, Y and Z will not be selected and vice-versa. In how many ways it can be done?
There are 10 person among whom two are brother. The total number of ways in which these persons can be seated around a round table so that exactly one person sit between the brothers , is equal to:
There are 10 person among whom two are brother. The total number of ways in which these persons can be seated around a round table so that exactly one person sit between the brothers , is equal to:
If letters of the work KUBER are written in all possible orders and arranged as in a dictionary, then the rank of the word KUBER will be:
If letters of the work KUBER are written in all possible orders and arranged as in a dictionary, then the rank of the word KUBER will be:
A man positioned at the origin of the coordinate system. the man can take steps of unit measure in the direction North, East, West or South. Find the number of ways of he can reach the point (5,6), covering the shortest possible distance.
A man positioned at the origin of the coordinate system. the man can take steps of unit measure in the direction North, East, West or South. Find the number of ways of he can reach the point (5,6), covering the shortest possible distance.
Ten different letters of alphabet are given, words with 5 letters are formed from these given letters. Then, the number of words which have at least one letter repeated is:
Ten different letters of alphabet are given, words with 5 letters are formed from these given letters. Then, the number of words which have at least one letter repeated is:
In the next World cup of cricket there will be 12 teams, divided equally in two groups. Teams of each group will play a match against each other. From each group 3 top teams will qualify for the next round. In this round each team will play against each others once. Four top teams of this round will qualify for the semifinal round, where they play the best of three matches. The Minimum number of matches in the next World cup will be:
In the next World cup of cricket there will be 12 teams, divided equally in two groups. Teams of each group will play a match against each other. From each group 3 top teams will qualify for the next round. In this round each team will play against each others once. Four top teams of this round will qualify for the semifinal round, where they play the best of three matches. The Minimum number of matches in the next World cup will be:
In a party every person shakes hands with every other person. If there are 105 hands shakes, find the number of person in the party.
In a party every person shakes hands with every other person. If there are 105 hands shakes, find the number of person in the party.
A teacher of 6 students takes 2 of his students at a time to a zoo as often as he can, without taking the same pair of children together more than once. How many times does the teacher go to the zoo?
A teacher of 6 students takes 2 of his students at a time to a zoo as often as he can, without taking the same pair of children together more than once. How many times does the teacher go to the zoo?
There are eight boxes of chocolates, each box containing distinct number of chocolates from 1 to 8. In how many ways four of these boxes can be given to four persons (one boxes to each) such that the first person gets more chocolates than each of the three, the second person gets more chocolates than the third as well as the fourth persons and the third person gets more chocolates than fourth person?
There are eight boxes of chocolates, each box containing distinct number of chocolates from 1 to 8. In how many ways four of these boxes can be given to four persons (one boxes to each) such that the first person gets more chocolates than each of the three, the second person gets more chocolates than the third as well as the fourth persons and the third person gets more chocolates than fourth person?
In how many ways can six different rings be worn on four fingers of one hand?
In how many ways can six different rings be worn on four fingers of one hand?
There are 6 equally spaced points A,B,C,D,E and F marked on a circle with radius R. How many convex pentagons of distinctly different areas can be drawn using these points as vertices?
There are 6 equally spaced points A,B,C,D,E and F marked on a circle with radius R. How many convex pentagons of distinctly different areas can be drawn using these points as vertices?
After every get-together every person present shakes the hand of every other person. If there were 105 handshakes in all, how many persons were present in the party?
After every get-together every person present shakes the hand of every other person. If there were 105 handshakes in all, how many persons were present in the party?
A college has 10 basketball players. A 5 member's team and a captain will be selected out of these 10 players. How many different selections can be made?
A college has 10 basketball players. A 5 member's team and a captain will be selected out of these 10 players. How many different selections can be made?
How many different five-letter words can be formed using the letter from the world APPLE?
How many different five-letter words can be formed using the letter from the world APPLE?
How many arrangements of four 0's (zeroes), two 1's and two 2's are there in which the first 1 occur before the first 2?
How many arrangements of four 0's (zeroes), two 1's and two 2's are there in which the first 1 occur before the first 2?
How many words can be formed by re-arranging the letters of the word ASCENT such that A and T occupy the first and last position respectively?
How many words can be formed by re-arranging the letters of the word ASCENT such that A and T occupy the first and last position respectively?
In how many ways can 8 Indians and, 4 American and 4 Englishmen can be seated in a row so that all person of the same nationality sit together?
In how many ways can 8 Indians and, 4 American and 4 Englishmen can be seated in a row so that all person of the same nationality sit together?
There are five cards lying on the table in one row. Five numbers from among 1 to 100 have to be written on them, one number per card, such that the difference between the numbers on any two adjacent cards is not divisible by 4. The remainder when each of the 5 numbers is divided by 4 is written down on another card (the 6th card) in order. How many sequences can be written down on the 6th card?
There are five cards lying on the table in one row. Five numbers from among 1 to 100 have to be written on them, one number per card, such that the difference between the numbers on any two adjacent cards is not divisible by 4. The remainder when each of the 5 numbers is divided by 4 is written down on another card (the 6th card) in order. How many sequences can be written down on the 6th card?
If 5* nP3 = 4* (n+1)P3, find n?
If 5* nP3 = 4* (n+1)P3, find n?
In how many ways a President, VP and Water-boy can be selected from a group of 10 people.
In how many ways a President, VP and Water-boy can be selected from a group of 10 people.
In how many ways can 10 examination papers be arranged so that the best and the worst papers never come together?
In how many ways can 10 examination papers be arranged so that the best and the worst papers never come together?
What is the total number of ways in which Dishu can distribute 9 distinct gifts among his 8 distinct girlfriends such that each of them gets at least one gift?
What is the total number of ways in which Dishu can distribute 9 distinct gifts among his 8 distinct girlfriends such that each of them gets at least one gift?
How many 5-digit positive integers exist the sum of whose digits are odd?
How many 5-digit positive integers exist the sum of whose digits are odd?
How many different words can be formed using all the letters of the word ALLAHABAD?
(a) When vowels occupy the even positions.
(b) Both L do not occur together.
How many different words can be formed using all the letters of the word ALLAHABAD?
(a) When vowels occupy the even positions.
(b) Both L do not occur together.
How many alphabets need to be there in a language if one were to make 1 million distinct 3 digit initials using the alphabets of the language?
How many alphabets need to be there in a language if one were to make 1 million distinct 3 digit initials using the alphabets of the language?
In a hockey championship, there are 153 matches played. Every two team played one match with each other. The number of teams participating in the championship is:
In a hockey championship, there are 153 matches played. Every two team played one match with each other. The number of teams participating in the championship is:
Find the total number of distinct vehicle numbers that can be formed using two letters followed by two numbers. Letters need to be distinct.
Find the total number of distinct vehicle numbers that can be formed using two letters followed by two numbers. Letters need to be distinct.
There are 7 non-collinear points. How many triangles can be drawn by joining these points?
There are 7 non-collinear points. How many triangles can be drawn by joining these points?
How many diagonals can be drawn in a pentagon?
How many diagonals can be drawn in a pentagon?
There are 10 points in a plane out of which 4 are collinear. Find the number of triangles formed by the points as vertices.
There are 10 points in a plane out of which 4 are collinear. Find the number of triangles formed by the points as vertices.
A tea expert claims that he can easily find out whether milk or tea leaves were added first to water just by tasting the cup of tea. In order to check this claims 10 cups of tea are prepared, 5 in one way and 5 in other. Find the different possible ways of presenting these 10 cups to the expert.
A tea expert claims that he can easily find out whether milk or tea leaves were added first to water just by tasting the cup of tea. In order to check this claims 10 cups of tea are prepared, 5 in one way and 5 in other. Find the different possible ways of presenting these 10 cups to the expert.
Find the number of triangles which can be formed by joining the angular points of a polygon of 8 sides as vertices.
Find the number of triangles which can be formed by joining the angular points of a polygon of 8 sides as vertices.
Jay wants to buy a total of 100 plants using exactly a sum of Rs 1000. He can buy Rose plants at Rs 20 per plant or marigold or Sun flower plants at Rs 5 and Re 1 per plant respectively. If he has to buy at least one of each plant and cannot buy any other type of plants, then in how many distinct ways can Jay make his purchase?
Jay wants to buy a total of 100 plants using exactly a sum of Rs 1000. He can buy Rose plants at Rs 20 per plant or marigold or Sun flower plants at Rs 5 and Re 1 per plant respectively. If he has to buy at least one of each plant and cannot buy any other type of plants, then in how many distinct ways can Jay make his purchase?
A letter lock consists of 4 rings, each ring contains 9 non-zero digits. This lock can be opened by setting four digit code with the proper combination of each of the 4 rings. Maximum how many codes can be formed to open the lock ?
A letter lock consists of 4 rings, each ring contains 9 non-zero digits. This lock can be opened by setting four digit code with the proper combination of each of the 4 rings. Maximum how many codes can be formed to open the lock ?
From a total of six men and four ladies a committee of three is to be formed. If Mrs. X is not willing to join the committee in which Mr. Y is a member, whereas Mr.Y is willing to join the committee only if Mrs Z is included, how many such committee are possible?
From a total of six men and four ladies a committee of three is to be formed. If Mrs. X is not willing to join the committee in which Mr. Y is a member, whereas Mr.Y is willing to join the committee only if Mrs Z is included, how many such committee are possible?
A man positioned at the origin of the coordinate system. the man can take steps of unit measure in the direction North, East, West or South. Find the number of ways of he can reach the point (5,6), covering the shortest possible distance.
A man positioned at the origin of the coordinate system. the man can take steps of unit measure in the direction North, East, West or South. Find the number of ways of he can reach the point (5,6), covering the shortest possible distance.
Out of eight crew members three particular members can sit only on the left side. Another two particular members can sit only on the right side. Find the number of ways in which the crew can be arranged so that four men can sit on each side.
Out of eight crew members three particular members can sit only on the left side. Another two particular members can sit only on the right side. Find the number of ways in which the crew can be arranged so that four men can sit on each side.
10 students are to be seated in two rows equally for the Mock test in a room. There are two sets of papers, Code A and Code B. each of two rows can have only one set of paper but different that from other row. In how many ways these students can be arranged ?
10 students are to be seated in two rows equally for the Mock test in a room. There are two sets of papers, Code A and Code B. each of two rows can have only one set of paper but different that from other row. In how many ways these students can be arranged ?
Out of eight crew members three particular members can sit only on the left side. Another two particular members can sit only on the right side. Find the number of ways in which the crew can be arranged so that four men can sit on each side.
Out of eight crew members three particular members can sit only on the left side. Another two particular members can sit only on the right side. Find the number of ways in which the crew can be arranged so that four men can sit on each side.
In how many ways 2 students can be chosen from the class of 20 students?
In how many ways 2 students can be chosen from the class of 20 students?
There are 2 brothers among a group of 20 persons. In how many ways can the group be arranged around a circle so that there is exactly one person between the two brothers?
There are 2 brothers among a group of 20 persons. In how many ways can the group be arranged around a circle so that there is exactly one person between the two brothers?
A family consist of a grandfather, 5 sons and daughter and 8 grandchildren. They are to be seated in a row for dinner. The grandchildren wish to occupy the 4 seats at each end and the grandfather refuses to have a grandchild on either side of him. The number of ways in which the family can be made to sit is:
A family consist of a grandfather, 5 sons and daughter and 8 grandchildren. They are to be seated in a row for dinner. The grandchildren wish to occupy the 4 seats at each end and the grandfather refuses to have a grandchild on either side of him. The number of ways in which the family can be made to sit is:
A team of 8 students goes on an excursion, in two cars, of which one can seat 5 and the other only 4. In how many ways can they travel?
A team of 8 students goes on an excursion, in two cars, of which one can seat 5 and the other only 4. In how many ways can they travel?
The number of positive integers which can be formed by using any number of digits from 0,1,2,3,4,5 without repetition.
The number of positive integers which can be formed by using any number of digits from 0,1,2,3,4,5 without repetition.
A box contains 10 balls out of which 3 are red and rest are blue. In how many ways can a random sample of 6 balls be drawn from the bag so that at the most 2 red balls are included in the sample and no sample has all the 6 balls of the same colour?
A box contains 10 balls out of which 3 are red and rest are blue. In how many ways can a random sample of 6 balls be drawn from the bag so that at the most 2 red balls are included in the sample and no sample has all the 6 balls of the same colour?
How many ways can 4 prizes be given away to 3 boys, if each boy is eligible for all the prizes?
How many ways can 4 prizes be given away to 3 boys, if each boy is eligible for all the prizes?
I have an amount of Rs 10 lakh, which I went to invest in stocks of some companies. I always invest only amounts that are multiples of Rs 1 lakh in the stock of any company. If I can choose from among the stocks of five different companies, In how many ways can I invest the entire amount that I have?
I have an amount of Rs 10 lakh, which I went to invest in stocks of some companies. I always invest only amounts that are multiples of Rs 1 lakh in the stock of any company. If I can choose from among the stocks of five different companies, In how many ways can I invest the entire amount that I have?
In a hockey championship, there are 153 matches played. Every two team played one match with each other. The number of teams participating in the championship is:
In a hockey championship, there are 153 matches played. Every two team played one match with each other. The number of teams participating in the championship is:
A committee is to be formed comprising 7 members such that there is a simple majority of men and at least 1 woman. The shortlist consists of 9 men and 6 women. In how many ways can this committee be formed?
A committee is to be formed comprising 7 members such that there is a simple majority of men and at least 1 woman. The shortlist consists of 9 men and 6 women. In how many ways can this committee be formed?
