i not getting the correct answer for this sum : In how many ways can five letters be placed in five envelopes such that exactly one letter goes into corresponding envelope?

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- November 6th 2009, 04:07 AMdukes123letter in envelope problem
i not getting the correct answer for this sum : In how many ways can five letters be placed in five envelopes such that exactly one letter goes into corresponding envelope?

- November 6th 2009, 04:18 AMPlato
- November 6th 2009, 05:37 AMHallsofIvy
Do you mean exactly one letter goes into each envelope?

You have 5 choices which letter to put into the first envelope, then 4 choices which to put in the second envelope, then 3, then 2, then 1. 5*4*3*2*1= 5!

This is exactly the same as the number of different ways to order 5 objects.

Plato's answer was assuming that each letter had a**correct**envelope and you were asking "how many ways can you put 5 letters in 5 evelopes if no letter goes into the correct envelope". I did not interpret your question that way. - November 6th 2009, 09:28 AMdukes123
hey plato your answer is correct

plz explain how u got D(4)=9 its little confusing for me :( - November 6th 2009, 10:36 AMPlato
Here is a very helpful website for derangements

Here is a formula: .

Here is a good approximation: .

, so - November 6th 2009, 10:59 PMdukes123
thks a lot !! got to learn somethin new today :)

- November 7th 2009, 04:32 AMHallsofIvy
Oh, I see now. "exactly one letter goes into corresponding envelope" means exactly one letter goes into the

**correct**envelope and the other four into the wrong envelopes.