Aptitude - Permutations and Combinations

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Question 1

If (n+1)p5 : (n)p6= 2:7 find n?

Question 2

(i)How many 4 letter words can be formed using the letters of the word 'ARTICLE'. (ii)Find the number of words begin with an vowel

Question 3

In how many ways 6 boys and 5 girls can be arranged along a row so that (i)all the girls come together (ii)no two girls come together (iii)no two of the same gender come together

Question 4

Find the number of ways of arranging 15 students A1,A2,...........A15 in a row such that A1,A2,A3 should sit together in a specified order.

Question 5

(i)Find the number of 4 digit numbers that can be formed using the digits 2,4,5,7,8 (ii)How many of them are divisible by (a)5 (b)25

Question 6

If the letters of the word PRISON are permuted in all possible ways and the words thus formed are arranged in dictionary order, find the rank of the word PRISON.

Question 7

If a set A has 6 elements, find the number of elements in the power set of A

Question 8

Find the number of proper divisors of 15! ?

Question 9

Find the number of zeros at the end of (100)!

Question 10

In how many ways can 10 men and 10 women be divided into 10 couples, each consisting of a man and woman.

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