Question

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

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

Answer 1

The correct option is C 7. ${}^6{C}_4{.}^8{C}_4$

Total letters = 11, No of S's = 4
First place 7 letters at lot place other than S = $\frac{7!}{4!2!}$
Now place S at X places such that no two S are adjacent
= $\frac{{}^8{P}_4}{4!}{=}^8{C}_4$
Hence, total number of arrangments
= $\frac{7!}{4!2!}$ X ${}^8{C}_4$ = 7. ${}^6{C}_4$ X ${}^8{C}_4$