Question

How many different anagrams can you form with the word POLYTECHNIQUE?

Answer 1

In the sense of any ordering of the `13` letters,
the answer is `(13!)/(2!) = 3113510400`

It would be `13!` except for the repeated letter 'E'.

Explanation:

Let the two E's be distinguished as `E_1` and `E_2`.

Then there are `13 xx 12 xx .. xx 1 = 13!` ways to order the letters.

There are `2!` ways to order `E_1` and `E_2` which can be applied to any of these `13!` orderings.

So since the two E's are not distinguished in the original problem, the number of distinct orderings is `(13!)/(2!)`