Question

The number of ways of writing the letters of ${}^{\prime }ASSASSI{N}^{\prime }$ in a row so that no two $S$ come together is

• A. $60$
• B. $120$
• C. $1440$
• D. None of these

Answer 1

Answer: (A)

$60$

Given: the word '$ASSASSIN$'

To find: the number of ways of writing the letters such that no two S comes together.

Sol: Total number of letters in the word = $8$

Number of S repeating= $4$

Number of A repeating = $2$

All the possible ways of forming a word are $8!$ = $\frac{8!}{4!2!}=840$

Letters other than S are$A,A,I,N.$

So, $\frac{4!}{(2!)}=12$.

The number of ways in which two $S$ do not come together:

1. $S$_$S$_$S$_$S$_

2. $S$_$S$_$S$_ _$S$

3. $S$_$S$__$S$_$S$

4. $S$_ _$S$_$S$_$S$

5. _$S$_$S$_$S$_$S$

Each arrangement of $A,A,I,N$ in the $5$ ways.

Hence, the number of ways of writing the letters such that no two S comes together $5\times 12=60.$