Question

In how many different unique ways can the letters of the word Statistically be arranged?

Answer 1

`(13!)/(2!3!2!2!2!)=(6,227,020,800)/(2xx6xx2xx2xx2)=64,864,800`

Explanation:

There are 13 letters in the word "statistically". If we had the letters ABCDEFGHIJKLM (all unique letters), there'd be

`13! = 6,227,020,800` ways to arrange the letters.

However, we have duplicate letters in "statistically" - there are 2 S's, 3 T's, 2 A's, 2 I's, and 2 L's. We divide the `13!` by the internal arrangements possible with all of the duplicates (there are `2!` ways to arrange two of something, `3!` ways to arrange 3 of something, etc). And so we have:

`(13!)/(2!3!2!2!2!)=(6,227,020,800)/(2xx6xx2xx2xx2)=64,864,800`