probability

First of all, when you ask what is the probability that exactly nineteen get their own number, if I'm not mistaken, is the same thing as all twenty get their own number.

If thats true... you multiply the probability that each individual person will get their own SID back.

The probability that the first person will get his/her SID back is 1/20. Now there's one less SID in the hat, and one less person who needs to choose.

So the probability that the next person gets his/her SID back is 1/19. Thus the probability that both the first person AND the second person get their SIDs back is (1/20)*(1/19).

You can see how to solve the problem now. Each person has a 1 in however many's left probability. And the 20th person will have a 1/1 chance to get theirs back because it'll be the only one. So you just multiply together all these probabilities.

Hope this helps.

I think this is intended as a trick question. It is impossible for exactly 19 people to get their own numbers, so the probability is zero.

It's probably just poorly formulated. 19 would be possible if each person replaced the object after drawing it. Bernoulli trials, which this is, are always calculable using binomial coefficients.

This is a fairly common riddle and is indeed a trick question.

Haha! It tricked me, that's obvious