How many different 11-letter words (real or imaginary) can be formed from the letters in the word MATHEMATICS?

Correct Answer is "4,989,600"

Explanation:

For this problem, we have n objects that are not distinct. The equation will provide us with the answer we need. There are a total of 11 letters. 3 of the letters are double letters, and the rest of the 6 are single letters.

There are 11! unique arrangements of 11 different objects (the objects in this case are letters). But since we have 2 A's, 2 I's and 2 N's, we must divide by the number of ways those can be rearranged creating indistinguishable combinations. That is 2! 2! 2!, meaning the answer is:

11! / (2! 2! 2!) = 4, 989, 600

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