Consider the following rearrangements of letters.

1. In how many distinct ways can the letters in the word ITEMS be arranged?

   Hint (a):

   A word with no repeated letters can be handled using a single factorial.

2. In how many distinct ways can the letters in the word STEMS be arranged?

3. In how many distinct ways can the letters in the word SEEMS be arranged?

   Answer (c):

   $\frac{5!}{2!2!} = 30$

4. What makes these counts different?