IMPORTANT NOTE: For these problems, don’t just give final result, show the steps

Question

IMPORTANT NOTE: For these problems, don’t just give final result, show the steps (e.g. if using multiplication principle instead of saying “5040”, show what you multiply by what: 10*9*8*7. You can actually leave it as that, calculating what’s it equals to isoptional and just a technicality.)

How many ways can n books be placed on k distinguishable shelves…

if the books are indistinguishable copies of the same title?

if no two books are the same, and the positions of the books on the shelves matter?

Explanation / Answer

1. Placing n books on k distinguishable shelves if all books are identical then we need to only choose k books to be placed on the shelves as the order of the books is not important here

So, C(n,k)

2. Here again we choose k books to be placed in C(n,k) ways but now the books are different from one another so there are k! permutations

So, C(n,k)k!

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