Question

Question #6828f

Answer 1

Well, you already know the answer. 27720 ways.

Explanation:

Instead of counting all the possibilities that do not of the P's together, you can count the number of ways with all P's together, then subtract it from the total number of possibilities.

Since there are 9 letters with 3P's and 2E's, you will use `(9!)/((2!)(3!))` which equals 30240.

To count the number of ways when all 3'Ps are together, simply consider the P's as one letter. For example, you could count PPPINEALE as P INEALE. Using this, there are total of 7 letters now with 2E's. Therefore, there are `(7!)/(2!)` or 2520 ways to arrange the letters with all of the P's together. Now, subtract 2520 from 30240 to find the final answer. ( which is 27720, of course.)

I hope that helped you understand ^&^