Permutations and Combinations questions
785 published questions with worked solutions.
- Let n be the number of ways in which 5 boys and 5 girls can stand in a queue in such a way that all the girls stand consecutively...
- Let n_1<n_2<n_3<n_4<n_5 be positive integers such that n_1+n_2+n_3+n_4+n_5=20. The number of such distinct arrangements...
- Words of length 10 are formed using the letters A,B,C,D,E,F,G,H,I,J. Let x be the number of such words where no letter is...
- Let n 2 be an integer. Take n distinct points on a circle and join each pair of points by a line segment. Colour the line segment...
- The number of integers greater than 6000 that can be formed using the digits 3,5,6,7 and 8 without repetition is
- Let S= 1,2,3, ,9 . For k=1,2, ,5, let N_k be the number of subsets of S, each containing five elements out of which exactly k are...
- A debate club consists of 6 girls and 4 boys. A team of 4 members is to be selected from this club including the selection of a...
- If all the words (with or without meaning) having five letters, formed using the letters of the SMALL and arranged as in a...
- Find the highest two digit prime factor of the number of divisors of the number a^7b^4c^2 ,d ,e ,f (excluding 1 and the number...
- Find the number of ways of distributing 16 prizes among three players such that each player gets at least three prizes.
- Find the exponent of 3 in 101!.
- If the number of four digit numbers with distinct digits is p and p=3^a2^b7^c, then evaluate a+b+c.
- The sum of all the divisors of the number n=1080 is k. Evaluate k 1000 .
- Between two junction stations A and B, there are 12 intermediate stations. Find the number of ways in which a train can be made...
- 3 prizes are to be given to 4 students. Find the number of ways of distributing these prizes so that no student gets all 3 prizes.
- Consider the word ALLAHABAD. Let p and q represent the number of words formed from the letters of the word ALLAHABAD in which...
- The total number of numbers that are formed from 0,1,2,3,4 which do not contain more than 20 digits is m^n, where m and n are one...
- Words are formed from the letters of the word BHARAT. If p and q represent the number of words having both A's together and the...
- Let the words formed by the letters of word OPTS be arranged in dictionary order. The ranks of words SPOT, POTS, STOP and POST...
- Consider the words formed from the letters of word CONSTANT. Let A be the set containing words having 2 N together and 2 T...
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