[DMunna]

In how many different ways can the letters in the letter in the word ARRANGEMENT be arranged?

[ebaines]

If the letters were all different the answer would be 11! but since the word contains some duplicates you need to reduce this. Here's how - note that there are 2 A's, so for each arrangement of the A's there are two "duplicates," hence you divide by 2. In general for each letter that occurs N times you divide by N! because that's how many ways those duplicates could be arranged. For example the word TEETHE has 2 T's and 3 E's, so the number of unique arrangements is 6!/(2! X 3!) = 60.