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In how many ways can the letters of the word "ASSASSINATION" can be arranged so that all S's are together?
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Verified Answer
The correct answer is:
$\frac{10 !}{3 ! 2 ! 2 !}$
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
$$
=\frac{4 ! 10 !}{3 ! 4 ! 2 ! 2 !}=\frac{10 !}{3 ! 2 ! 2 !}
$$
$$
3 \text { A's, } 4 \text { S's, } 2 \text { I's, } 2 \text { N's, } 1 \text { T's, } 1 \text { O's }
$$
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
$$
=\frac{4 ! 10 !}{3 ! 4 ! 2 ! 2 !}=\frac{10 !}{3 ! 2 ! 2 !}
$$
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