Anyone good at advanced statistics?

[beez7777]

my friend asked for my help with a question, but i haven't taken statistics yet and have no idea how to answer it, but i figured someone here would know. if he gets the answer, he gets an automatic 100 on his final tomorrow.

61 students take a test, randomly give them back to the teacher. The teacher randomly gives the tests back to the students. What is the probability that k # of students get their own test back?

[clayj]

I think your question was just a TAD unclear... let's restate it.

61 students take a test. They hand them back to the teacher in no particular order. The teacher shuffles them, so they're truly in random order, and then hands them back to the students, again in no particular order. So, each student now has one of 61 tests.

Given that scenario, what exactly is it you want to know?

[swiftaw]

the probability that k out of 61 will get their own test is:

(1/61!)* sum for j = 0 to 61-k of [((-1)^j)/j!]

hope this makes sense, best I can do without the ability to use math symbols.

If you need a more detailed explanation of where the answer comes from, let me know.