Question

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

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

Answer 1

Answer: (D)

First of all arrange $M, I, I, I, I, P, P$
This can be done in $\frac{7\,!}{4\,!\, 2\,!}$ ways.
$\times M \times I\times I\times I\times I\times P\times P\times$
If we place is $S$ at any of the $X$ places then no two $S’s$ are together.
$\therefore $ total number of ways $=\frac{7\,!}{4\,!\, 2\,!}\cdot^{8}C_{4}$
$=7\times\,{}^{6}C_{4}\times\,{}^{8}C_{4}$ ways.