# Cycle of length

I'm learning permutations and came upon this question which made me freeze. So to say it in my own words, it asks that how many permutations in $S_n$ do not have a cycle of length one in their disjoint cycle notation. My guess at it would be just one but I don't know how to show it.

• Have you tried writing down all the permutations of $S_3$ as products of disjoint cycles? – Paul Gustafson Apr 10 '13 at 14:18
• Tough problem, if you are meeting it fresh. Look at the wikipedia article on Derangements. – André Nicolas Apr 10 '13 at 14:22
• @AndréNicolas I looked at Derangments but it confused me further. I can see the connection to a certain limit but Im not able to solve for this problem. – user65422 Apr 14 '13 at 23:48
• @user66345 Like this? $(a,b,c)=(a,c),(a,b)$ – user65422 Apr 15 '13 at 1:18