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Combinations, Permutations and Cycles

How many elements of order 5 are there in S_8?
- I think there are 8! / 3!5! = 56 ways to order the elements in the cycle but how many of order 5 are there?

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We know, each element in S_8 can be expressed as a product of disjoint cycles. If an element has order 5, then each cycle of this element ...

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The number of elements of order 5 in S_8 is determined. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.