Secret Santa Odds?

Secret Santa Odds?
If you are doing a Secret Santa gift game with 25 people, what are the odds of picking your own name? Let's assume everyone writes their own name on a slip of paper, tosses it into a hat, and then everyone pulls a name from the hat. What are the total odds that one of the 25 people would pull their own name from the hat? TO CLARIFY: I am asking the odds that when all 25 people open their slips of paper, what is the likelihood that ANY ONE of them has pulled their own name. Not the odds for any one individual (1/25), but for the group as a whole. Thanks! I mean AT LEAST one person pulling their own name. I mean AT LEAST one person pulling their own name.


Answers:

ewanog:  25 factorial, aka 25! which ends up being 1.551121 ?10^25 i could be wrong, but it seems logical
2007-12-07 13:56:03
Northstar:  Once the group gets above about the size of 10, the odds hardly change at all. The odds of at least one person drawing their own name is very close to 1 - 1/e ? .632
2007-12-07 14:21:01
SM:  Good question! Btw, when you say any one, do you mean AT LEAST one or EXACTLY one. Northstar, how would one go about solving such a problem? If you have to consider the probability of exactly one person pulling his/her own name, it would be something like this, I guess. Probability of 1 person pulling own name = 1/25 Probability of 2 person NOT pulling own name = 23/25 Probability of 3 person NOT pulling own name (would depend on whether 2 has/has not picked 3). So this gets more and more complicated. Would really appreciate if someone could explain how to solve this!!
2007-12-07 15:10:03