SOLUTION: How many different permutations of the letters in the word CINCINNATI are there?

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Question 1051106: How many different permutations of the letters in the word CINCINNATI are there?
Found 2 solutions by stanbon, ikleyn:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
How many different permutations of the letters in the word CINCINNATI are there?
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10!/(2!*3!*3!) = 50400
Cheers,
Stan H.
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Answer by ikleyn(52776) About Me  (Show Source):
You can put this solution on YOUR website!
.
How many different permutations of the letters in the word CINCINNATI are there?
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10%21%2F%28%282%21%29%2A%283%21%29%2A%283%21%29%29 = 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.