posted by Chris on .
Hi, I hope you guys don't mind if I post a couple probability questions.
A child returns a five-volume set of books to a bookshelf. The child is not able to read, and so cannot distinguish one volume from another. What is the probability that the books are shelved in the correct order?
If a six-sided die is rolled six times, what is the probability that each side appears exactly once?
there are 5! ways or 120 ways to arrange the books, but only one is the correct one.
so the prob. is 1/120
for the second:
let's consider one of the ways:
numbers show up: 1,2,3,4,5,6
the prob of that happening = (1/6)*(1/6)..(1/6) six times
but it did not have to come up in that order, as a matter of fact there are 6! ways for the 1,2,3,4,5,6 to come up or 720 ways
so prob of your event = 720*(1/6)^6 = 720/46656