### Instruction: Determine the number of ways to arrange the letters of the word THAT.### Response: To arrange the letters of a word, I need to consider how many positions there are and how many choices I have for each position.
In this case, the word THAT has four positions, so I might start by thinking that there are 4! = 24 ways to arrange the letters.
However, this would overcount some arrangements, because the word THAT has two identical letters, T.
This means that swapping the two T's does not create a new arrangement, but my 4! calculation would count it as one.
To avoid this overcounting, I need to divide by the number of ways to arrange the identical letters among themselves.
In this case, there are two T's, so there are 2! = 2 ways to arrange them.
Therefore, the number of ways to arrange the letters of the word THAT is 4! / 2! = 24 / 2 = 12.