Question

How many different words can be formed by jumbling the letters in the word 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)

$7\cdot\,^6C_4\cdot\,^8C_4$

Answer 2

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 $S??$ 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.