Question

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

Answer 1

`38949120` words can be formed , in which no two "S"
are adjacent.

Explanation:

Number of letters in the word "MISSISSIPPI" is `11` of which

number of "S" are `4`. Let us consider the number of ways ,

where all four "SSSS" always occur together. We assume

"SSSS" as a single letter , then the umber of letters in the word

"MISSISSIPPI" becomes `8`. Hence they can be arranged in

`8 !` ways . Four "SSSS" can be arranged among themselves

in `4!` ways. Total number of words can be formed in

`T_s = 8! *4! =40320*24=967680` ways taking all "S' together.

In `11` letters they can be arranged in `T=11! =39916800`

ways. Number of jumbled words in which no two "S"are adjacent

is `J= T - T_s= 39916800-967680= 38949120` [Ans]