1) Which permutations from Problem 1 and Problem 2 are cycles and which are transpositions? 2) How many cycles of length $57$ are there in the set $S_{57}$? 3) How many cycles and how many transpositions are there in $S_{5}$? 4) When the product of two transpositions is a cycle? 5*) When the product of two cycles is a cycle?
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