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Permutation $\tau$ has only cycles with two and three elements. It has four cycles with two elements and five cycles with three elements. Find the number of all permutations $\sigma$ such that $\sigma^4=\tau$.

I completely don't know how to approach. I think decomposition of permutation into cycles is crucial but don't know how to exactly use it.

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    @RagibZaman: It can be deduced from the question (assuming that "only cycles with two and three elements" implies there can be no fixed points, which is true in the combinatorial interpetation of "cycles") that $\tau$ is a permutation of $4\times2+5\times3=23$.2012-09-10
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    @MarcvanLeeuwen Ah yes. I'll delete that comment then. Thanks.2012-09-10
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    The sections on Permutations in Stanley's Enumerative Combinatorics and Wilf's Generatingfunctionology both have methods for solving this type of problem. Both are available freely online on their authors respective webpages.2012-09-10

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