Question 1051106
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How many different permutations of the letters in the word CINCINNATI are there?
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{{{10!/((2!)*(3!)*(3!))}}} = 50400.


In all, there are 10 letters in the word.
Of them, C is repeated 2 times, I is repeated 3 times, and N is repeated 3 times.
The rest of the letters are unique.

The factors in the denominator, from left to right, are:

2! in the denominator is for C which is repeated 2 times in the word;
3! in the denominator is for I which is repeated 3 times in the word;
3! in the denominator is for N which is repeated 3 times in the word.
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