Question

In how many distinct ways can the letters of the word STATES be arranged?

Answer 1

180

Explanation:

If we had 6 unique letters, such as STABLE, we'd be able to arrange the letters in `6! = 720` ways (we'd have 6 choices of what the first letter could be, 5 for the next letter, 4 for the next, etc... giving `6xx5xx4xx3xx2xx1 = 6!`

In our case, we have 2 sets of letters where there are more than 1 - we have two S's and two T's. And so we have to divide out the number of ways each of them can order `(S_1TATES_2` is the same as `(S_2TATES_1)` and so we'll have:

`(6!)/(2!2!)=(6xx5xx4xx3xx2!)/(2xx2!)=180`