Question

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

• A. $(8)\left({}^6{C}_4\right)\left({}^7{C}_4\right)$
• B. (6) (7) $\left({}^8{C}_4\right)$
• C. $(6)(8)\left({}^7{C}_4\right)$
• D. $(7)\left({}^6{C}_4\right)\left({}^8{C}_4\right)$

Answer 1

Answer: (D)

We can permute $M,I,I,I,I,P,P$ in $\frac{7!}{4!2!}$ ways. Corresponding to each arrangement of these seven letters, we have 8 places where $S$ can be arranged as shown below with $X$.
$X\square X\square X\square X\square X\square X\square X\square$
We can choose 4 places out of 8 in ${}^8{C}_4$ ways. Thus, the required number of ways
$=\left({}^8{C}_4\right)\left(\frac{7!}{4!2!}\right)=(7)\left({}^8{C}_4\right)\left({}^6{C}_4\right)$