### Instruction: Determine the number of ways to arrange the letters of the word TARTAR.### Response: To arrange the letters of a word, I can use the formula for permutations of n objects, where some are identical.
The formula is n! / (k1! * k2! * ... * km!), where n is the total number of objects, and k1, k2, ..., km are the numbers of identical objects of each type.
In this case, n = 6, since there are six letters in TARTAR.
There are two identical letters of type A, two identical letters of type R, and two identical letters of type T.
So, k1 = k2 = k3 = 2.
Plugging these values into the formula, I get 6! / (2! * 2! * 2!) = 90.
Therefore, there are 90 ways to arrange the letters of the word TARTAR.