Combinatorics (Partitioning books onto shelves)

[tdschenk]

Homework Statement

45.) Twenty different books are to be put on five book shelves, each of which holds at least twenty books.
a) How many different arrangements are there if you only care about the number of books on the shelves (and not which book is where)?
b) How many different arrangements are there if you care about which books are where, but the order of the books on the shelves doesn't matter?
c) How many different arrangements are there if the order on the shelves does matter?

Homework Equations

For part (a)

I know that the equation for separating objects into unlabeled partitions is

n!/(k!)(n1!)(n2!)..(nk!)

where n1,n2,etc. are the number of objects in each partition and k is the number of partitions, but I don't know where to go from there. Is this the right idea? Hopefully if someone can help me with (a) i can figure out the other parts of the problem.

 

[tdschenk]

Alright. I found the answer to (a) to be 10626 and am quite confident I am correct, and (c) is just that answer*(20!).

Now I am stuck on part (b). Any hints would be appreciated.

 

[awkward]

(b) Suppose you make a list of the books and write, next to each book, the number of the shelf it's on.

 

[tdschenk]

Ahh right, I guess I just got mixed up on the wording. When you say it like that, I got it right away. Ha ha, thanks!