Show that the number of permutations of $n$ numbers, for $n \ge 2$, with two cycles is at most $(n - 1)!(\log(n - 1)+1)$, where $\log$ denotes the natural logarithm. Justify your answer.
I assume we would use a summation at some point, but I'm unsure as to where. I have tried using notes I have made on this topic but can't seem to find anything that directly relates to this question. Could someone also explain the concept of a permutation cycle and cycle lengths as these are things I don't fully understand. Thank you in advance.