Question

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

• A. $8{\times }^6{C}_4{\times }^7{C}_4$
• B. $6\times 7{\times }^8{C}_4$
• 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 $7{\times }^6{C}_4{\times }^8{C}_4$

Other than S, seven letters M, I, I, I, P, P, I can be arranged in $\frac{7!}{2!4!}=7\times 5\times 3$ ways.
Now four S can be placed in eight spaces (gaps) in ${}^8{C}_4$ ways.
Desired number of ways
$7\times 5\times 3{\times }^8{C}_4=7{\times }^6{C}_4{\times }^8{C}_4$