Question

How many distinct ways can the eleven letters in the word "TALLAHASSEE" be arranged?

Answer 1

`831600`

Explanation:

11 letters can be rearranged in 11! ways.

However, in TALLAHASSEE, there are 3 A's 2 L's, 2S's and 2E's. Rearranging any of these repeated letters among themselves do not change the resulting word.

Such rearrangements can be done in `3!times 2!times 2!times!` ways. Thus, each distinct word is counted `3!times (2!)^3` in the `11!` rearrangements.

Thus the number of distinct words is

`(11!)/(3!times (2!)^3) =831600`