Question

How many different words can be formed by jumbling the letters in the word 'MISSISSIPPI' in which no two S are adjacent?

• A. $7\times {}^{6}C_4\times {}^{8}C_4$
• B. $8\times {}^{6}C_4\times {}^{7}C_4$
• C. $6\times 7\times {}^{8}C_4$
• D. $6\times 8\times {}^{7}C_4$

Answer 1

The correct option is A

$7\times {}^{6}C_4\times {}^{8}C_4$

Explanation of the correct option :

Step1. Giving word $\mathit{M}\mathit{I}\mathit{S}\mathit{S}\mathit{I}\mathit{S}\mathit{S}\mathit{I}\mathit{P}\mathit{P}\mathit{I}$:

Given, that $MISSISSIPPI$ is the word

Where letter $I=4$ times, letter $S=4$times, letter $P=2$ times and $M=1$ times

First of all, arrange $M,I,I,I,I,P,P$
This can be done in $\frac{7!}{2!\times 4!}$ ways.

Step 2. Apply the condition of placing the word :

$\times M\times I\times I\times I\times I\times P\times P\times$
If we place is $S$ at any of the $\times$ places then no two $S’s$are together.
$\therefore$ total number of ways $=\frac{7!}{2!\times 4!}\times {}^{8}C_4$
$=7\times {}^{6}C_4\times {}^{8}C_4$ways.

Hence the correct option is A.