IMPORTANT NOTE: For these problems, don’t just give final result, show the steps
ID: 3011742 • Letter: I
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!