Question

How many different words can be formed by the letters of the word $MISSISSIPPI$ in which number two are adjacent ?

• A. $8\times {}^{6}C_4\times {}^{7}C_4$
• B. $2\times 7\times {}^{8}C_4$
• C. $6\times 8\times {}^{7}C_4$
• D. $7\times {}^{6}C_4\times {}^{8}C_4$

Answer 1

The correct option is D

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

Explanation for the correct option:

Find the required number of ways:

Given word is $MISSISSIPPI$

Leaving $S$, we have $7$ letters $M,I,I,I,P,P,I$

Now, Number of ways of arranging them $=\frac{7!}{2!4!}$

$=7\times 5\times 3$

Also, four $S$ can be put in $8$ places in ${}^8{C}_4$ ways.

$\therefore$The required number of ways $=7\times 5\times 3\times {}^{8}C_4$

$=\mathbf{7}\mathbf{}\mathbf{\times }\mathbf{}{}^{\mathbf{6}}\mathit{C}_{\mathbf{4}}\mathbf{}\mathbf{\times }\mathbf{}{}^{\mathbf{8}}\mathit{C}_{\mathbf{4}}$

Hence, Option ‘D’ is Correct.