Hundred different books are put on ten book shelves,each of which holds at least

Question

Hundred different books are put on ten book shelves,each of which holds at least hundred books.

(A) How many different arrangements are there if you only care about the number of books on the shelves? Do not use 12-ways formula

(B) How many different arrangements are there if you care about which books are where,but the order of the books on the shelves doesn't matter? Do not use 12-way formula.

(C) How many different arrangements are there if the Oder on the shelves does matter? Do not use 12-way formulas.

Explanation / Answer

(a) This problem is equivalent to distributing 100 items to 10 containers.

This can be done in (100+10-1) C (10-1) = 109C9 ways.

(b) Each book has 10 choices.

Since there are 100 books, this can be done in 10100 ways.

(e) Each book has 10 choices and all the books can permute in 100! ways.

Number of ways to arrange = 10100 * 100!.

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