SOLUTION: How many different permutations can be formed using all the letters in the word MASSACHUSETTS?

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Question 1046387: How many different permutations can be formed using all the letters in the word MASSACHUSETTS?

Answer by ikleyn(52884) About Me  (Show Source):
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How many different permutations can be formed using all the letters in the word MASSACHUSETTS?
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The word MASSACHUSETTS contains 13 letters, of them "S" is repeating 4 times, "A" is repeating 2 times, "T" is repeating twice. 
The remaining letters are unique.


13 symbols create 13! permutations.

Of them, the number of distinguishable permutations is 13%21%2F%284%212%212%21%29 = %2813%2A12%2A11%2A10%2A9%2A8%2A7%2A6%2A5%29%2F%282%2A2%29 = 13*12*11*10*9*2*7*6*5 = 64864800.

We divide 13! by k! for each symbol in the word repeating k times.

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