Question

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

• A. ${\mathrm{6.8.}}^7{C}_4$
• B. ${7.}^6{C}_4{.}^8{C}_4$
• C. ${8.}^6{C}_4{.}^8{C}_4$
• D. ${6.7}^8{C}_4$

Answer 1

Answer: (B)

${7.}^6{C}_4{.}^8{C}_4$

We have to remove all "S" from word MISSISSIPPI so,
We could put 4 "S" on 8 places so
${}^8{C}_4$
After removing all 'S' it is : 'M'I'I'I'P'P'I'
now we have to permute it so $\frac{7!}{4!\times 2!}$
Total Cases will be $=$ ${}^8{C}_4\times \frac{7!}{4!\times 2!}$ $=$ ${7.}^6{C}_4{.}^8{C}_4$