In how many ways can the letters of the word ASSASSINATION be arranged so that all the S’s are together?

Solution:

We know that the number of arrangements (permutations) that can be made out of n things out of which there are p, q, r, ... number of repetitions = n! / [p! q! r! ...].

In the given word ASSASSINATION,

No. of A's = 3
No. of N's = 2
No. of S's = 4
No. of I's = 2
Total number of letters = 13. 

If we consider all the four S's together, then there will be 10 units as follows:

A, A, I, N, A, T, I, O, N, SSSS

Here, there are 3 A's, 2 N's, and 2 I's that are repeated.

Thus, the required number of ways

= 10!/(3! 2! 2!)

= 151200

NCERT Solutions Class 11 Maths Chapter 7 Exercise ME Question 11

In how many ways can the letters of the word ASSASSINATION be arranged so that all the S’s are together?

Summary:

The number of ways in which the letters of the word ASSASSINATION can be arranged so that all the S’s are together is 151200