1. The problem statement, all variables and given/known data How many elements of each cycle-type are there in S5? 3. The attempt at a solution One way of working this out would be to write out each permutation and see how many 2-cycles, 3-cycles ,4-cycles and 5-cycles there are but given that there are 5! permutations this would take very long. Does anybody know of an easier way to see the answer?