A classic counting problem is to determine the number of different ways that the letters of "embarrass" can be arranged. Find that number.
The number of different ways that the letters of "embarrass" can be arranged is (Simplify your answer.)

Step 1 ：The word 'embarrass' has 9 letters, with the letter 's' repeating 3 times, 'r' repeating 2 times, and 'e' repeating 2 times. The rest of the letters are unique.

Step 2 ：The number of ways to arrange n items, where some items are identical, is given by the formula \(\frac{n!}{r1! * r2! * ... * rk!}\), where n is the total number of items, and r1, r2, ..., rk are the numbers of each type of identical item.

Step 3 ：In this case, n = 9, r1 = 3 (for 's'), r2 = 2 (for 'r'), and r3 = 2 (for 'e').

Step 4 ：So, the number of ways to arrange the letters of 'embarrass' is \(\frac{9!}{3! * 2! * 2!}\).

Step 5 ：By simplifying the above expression, we get the number of arrangements as 15120.

Step 6 ：Final Answer: The number of different ways that the letters of 'embarrass' can be arranged is \(\boxed{15120}\).