# 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?

Apr 20, 2017

$120$

#### 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.