Kenneth Rosen Edition 7 Exercise 6.5 Question 13 (Page No. 432)

Question

A book publisher has $3000$ copies of a discrete mathematics book. How many ways are there to store these books in their three warehouses if the copies of the book are indistinguishable?

Answer 1

Quickie way to do this: Lay 3000 books in a row, and put two walls anywhere between the books or at the ends, such that the 2 walls are not in the same place. The 2 walls partition the row of books into 3 sections which then go to the 3 bookstores.

C(3+3000-1, 3000) = C(3002, 2) = 4504501

Note: there are 2 ways of thinking about this, which arrive at 2 equivalent formulas:

C(n+k-1, k-1) or C(k+n-1, n)

Try to think of 2 reasons the answer is 4504501