Combinatorics: how many ways to organize $4$ books in $7$ different boxes?

Question

I'm trying to figure out this problem in combinatorics and can't seem to find the right approach: If you have $4$ books and $7$ boxes, where each box can contain several books (or none) - how many possibilities are there to organize said books in the boxes?

I think I should use the binomial equation somehow, but can't figure it out.

Would really appreciate your guidance.

Thank you.

Answer 1

HINT:

Assuming the books are distinguishable then think how many possibilities you have for the first book, then for the second and so on.

Assuming the books are undistinguihable then read up on stars and bars

Hope this helped