Determine the number of ways to arrange the letters of the word TOOT.
I notice that the word TOOT has two O's and two T's, so I cannot simply use the formula n! for the number of permutations of n distinct objects. Instead, I need to account for the fact that swapping the two O's or the two T's does not produce a new arrangement. One way to do this is to divide n! by the product of the factorials of the number of times each letter repeats. In this case, n = 4, since there are four letters in TOOT. The letter O repeats twice, so I divide by 2!. The letter T also repeats twice, so I divide by another 2!. Therefore, the number of ways to arrange the letters of the word TOOT is 4! / (2! * 2!) = 6. 