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How many distinguishable permutations can be made of the letters in the word STEGOSAURUS?
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The given word contains 11 letters.
Of them, the letter S is repeated 3 times, and
the letter U is repeated 2 times.
The rest of the letters are unique.
So, the number of distinguishable permutations is = 3326400.
We divide the total number of permutations of 11! by 3!, because all permutations that permute the letter S only, lead to indistinguishable arrangements.
We divide the total number of permutations of 11! by 2!, because all permutations that permute the letter U only, lead to indistinguishable arrangements, too.
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On Permutations, see the lessons
- Introduction to Permutations
- PROOF of the formula on the number of Permutations
- Problems on Permutations
in this site.