Question

How do you find the number of permutations of all the letters of the word SCISSORS which you have no two letters S,S consecutive?

Answer 1

`120`

Explanation:

Apart from the letter "S", all of the other letters in "SCISSORS" are unique.

Writing "?" for letters from "CIOR", the permissable permutations take one of the following forms:

"S?S?S?S?"

"S?S?S??S"

"S?S??S?S"

"S??S?S?S"

"?S?S?S?S"

These `5` permissable arrangements are independent of the sequence of `4` letters of "CIOR" which occur where the "?"'s are.

So there are a total of:

`5 * 4! = 120`

permissible permutations.