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How many distinct four-letter permutations are possible using four of the ten letters in MATHCOUNTS?

 Nov 7, 2023
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There are (410​)=210 ways to choose which 4 letters to use out of the 10 letters in MATHCOUNTS.

Once we have chosen our 4 letters, we can permute them in 4! ways.

Therefore, there are 210×4!=5040​ distinct four-letter permutations that can be formed using four of the ten letters in MATHCOUNTS.

 Nov 7, 2023

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