How many different ways can the letters of "statistics" be arranged? The number of different ways that the letters of "statistics" can be arranged is (Simplify your answer.)

Step 1 ：The word 'statistics' has 10 letters in total. Among these, the letter 's' appears 3 times, the letter 't' appears 3 times, the letter 'i' appears 2 times, and the letters 'a' and 'c' appear once each.

Step 2 ：The number of different 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 = 10, r1 = 3 (for 's'), r2 = 3 (for 't'), r3 = 2 (for 'i'), r4 = 1 (for 'a'), and r5 = 1 (for 'c').

Step 4 ：Substituting these values into the formula, we get \(\frac{10!}{3! * 3! * 2! * 1! * 1!} = 50400\).

Step 5 ：Final Answer: The number of different ways that the letters of 'statistics' can be arranged is \(\boxed{50400}\).