So I'm trying to answer this question and am not sure if my answer is correct. In the text book I'm using, this question asked before combinations are even introduced (only permutations) so I'm not entirely sure if I'm in the right direction. Is it possible to answer these using permutations?
Consider a bookcase with 6 shelves and suppose that we have 15 different books to place on the selves. How many different ways are there to place the books on the shelves if the left to right order on each shelf is unimportant?
The order being unimportant implies it's a combination question, and having different "containers" lead me to use the stars and bars approach.
C(n + k -1, k) = C(5 + 15, 15) = C(20,15) ways to put the puts on the shelf when order is unimportant.
The next part of the question says the order is important, assuming the above answer is right, would the number of ways with order simply be 15! * C(20, 15)? Furthermore if each shelf is to get at least one book, is C(14, 9) correct when order is unimportant?
Some confirmation or correction would be appreciated, as would alternate methods for solving. Thanks!