Question

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?

Thanks.

Answer 1

there are 5! ways or 120 ways to arrange the books, but only one is the correct one.
so the prob. is 1/120

Answer 2

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
= (1/6)^6

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
=5/324