In how many ways can the letters of the word "ASSASSINATION" can be arranged so that all S's are together?
In how many ways can the letters of the word "ASSASSINATION" can be arranged so that all S's are together?
10 !
$\frac{10 !}{3 ! 2 ! 2 !}$
$\frac{9 !}{3 ! 2 ! 2 !}$
9 !
Solution
There are total 13 letters in the word "ASSASSINATION"
$
3 \text { A's, } 4 \text { S's, } 2 \text { I's, } 2 \text { N's, } 1 \text { T's, } 1 \text { O's }
$
Let all $S^{\prime}$ be represented by a single letter Z New word is AAINAIONZ.
$\therefore$ Total number of ways of forming a way taken all S's are together
$
=\frac{4 ! 10 !}{3 ! 4 ! 2 ! 2 !}=\frac{10 !}{3 ! 2 ! 2 !}
$