2
$\begingroup$

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.

  • 0
    Something less abstract than envelopes and letters. Ten married couples. All $20$ people are dancing, in pairs. Could *exactly* $9$ women be dancing with their husbands? Who is left over for the $10$th woman to dance with?2011-08-30

1 Answers 1

6

If nine letters go into the correct envelopes, what can you say about the remaining 1 letter?

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
    $0$,thanks a lot for your inputs :-)2011-08-30