Question

A classic counting problem is to determine the number of different ways that the letters of “dissipate” can be arranged. Find that number

Answer 1

90720 ways

Explanation:

Since there are 9 letters, there are 9! ways to arrange them. However since there are repeating letters, we have to divide to remove the duplicates accordingly. There are 2 ‘s’ and 2 ‘i’ hence:

Number of way to arrange ‘dissipate’ = 9! / (2! x 2!) = 90720 ways

Hence there are 90720 ways to have the number of dissipate in the letter.