Anagrams of ANAPLAN

How many different anagrams of ANAPLAN are there?

There are \displaystyle \frac{7!}{3!2!} anagrams of ANAPLAN.

@asmith42

True that! I do wonder why, though?

I believe its because if you want to make an anagram of a word without repeating letters, it would simply be n!. There are n options for what to choose for the first letter, there are n-1 options for the next, and so on. ANAPLAN has 3 a’s and 2 n’s, which makes it more complicated. If we just use 7!, it will include anagrams that are the exact same, just with the a’s or n’s swapping places with the other a’s or n’s, which don’t affect the word. To fix this we divide 7! by 3!2!.

I think this would be 7!/(3!2!)