Question

A classic counting problem is to determine the number of different ways that the letters of "embarrass""embarrass" can be arranged. find that number

Answer 1

Total number of letters in word "embarrass" = 9
Following letters are repeated:
Letter a occurs 2 times
Letter r occurs 2 times
Letter s occurs 2 times

The number of different ways the letters of word embarrass can be arranged can be calculated using permutations. The total number of different ways the letters of "embarrass" can be arranged will be:

$\frac{9!}{2!*2!*2!}=45360$

Thus there are 45360 different ways to arrange the letters of the word embarrass.