Five men are trying to find their hats in a closet. The closet contains their hats as well as 5 additional hats. (total 10 hats) What is the probability that at least one man retrieves his own hat?

Thank you for your help.

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- Mar 17th 2010, 10:33 AMJoAdams5000Looking for Hats
Five men are trying to find their hats in a closet. The closet contains their hats as well as 5 additional hats. (total 10 hats) What is the probability that at least one man retrieves his own hat?

Thank you for your help. - Mar 17th 2010, 12:50 PMAnonymous1
If there are men and hats. The probability that men select there own hat is:

Where, is the probability that no matches occur.

For your case, extend the number of hats to and let to be then to be Now take minus the sum of your values for and

Hope this helps.

Anonymous - Mar 17th 2010, 02:35 PMAnonymous1
I derived the formula above through recursion. I didn't type it out because I'm lazy. But, I just realized if you wanna be slick about it.

k men select there own hat ~

Booyah-Kasha (Cool).

Anonymous - Mar 17th 2010, 04:15 PMPlato
- Mar 17th 2010, 04:20 PMAnonymous1
- Mar 17th 2010, 04:33 PMPlato
- Mar 17th 2010, 04:42 PMAnonymous1
That came off wrong. I wasn't knocking your solution, I was saying that instead of considering the sum from 1 to 5, consider 1 minus the sum of 0 and 1.

Well can you see why it would ~ - Mar 17th 2010, 04:57 PMPlato