Question

How many different 9-letter

arrangements are possible using
the letters in the word DISAPPEAR?

Answer 1

`(9!)/(2!2!)=(3\cdot4\cdot5\cdot6\cdot7\cdot8\cdot9)/(2)=90720`

`9!` is the number of arrangements of all 9 letters, but since the same letters are indistinguishable, we divide by the number of their permutations. And there are two instances of two different letters, hence
`2!2!`.