# In how many ways can $10$ letters be placed in $10$ addressed envelope such that exactly $9$ letters are in correct envelope?

I have one problem which goes like this: "In how many ways can $10$ letters be placed in $10$ addressed envelope such that exactly $9$ letters are in correct envelope?"

If I understand the problem correctly this is similar to counting derangement with exactly $r$ matches,I don't know how to do it,please help.

• Zero? The tenth letter should go into the correct envelope as well. Aug 30, 2011 at 13:59
• I don't have the answer/solution for this one. Aug 30, 2011 at 14:01
• There is less to this problem than meets the eye. Aug 30, 2011 at 14:02
• @André Nicolas:Pardon,what exactly do you mean? Aug 30, 2011 at 14:03
• possible duplicate of How many fixed points in a permutation Aug 30, 2011 at 14:05

The following is not necessary for solving this problem, but I am adding it since you mentioned derangements and number of permutations with exactly $k$ matches (aka fixed points). The more general problem is to find the number of permutations with exactly $k$ fixed points. The solution for this is described in this wikipedia page.
• $0$,thanks a lot for your inputs :-) Aug 30, 2011 at 14:15