Question

Find the number of unique permutations of the letters in the word: EXTENT

720
180
900
36

Answer 1

180

Explanation:

A word has n letters.

There are m repeating letters, each of them repeating
`r_(0), r_(1), ..., r_(m)` times

So the number of distincts ways the letters can be permutated is:

`N_(A) = (n!)/(r_(1)! * r_(2)! * ... * r_(m))`

In this question:

Extent has 6 letters.

E and r repeat 2 times. So

`N = (6!)/(2!*2!) = 180`

So the answer is 180.