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

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How many ways can n books be placed on k distinguishable shelves?
a. If no two books are the same ,and the positions of the books on the shelves does not matter?
b. If no two books are the same,and the positions of the books on the shelves matter?

posted Jun 11, 2017 by anonymous

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1 Answer

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If there are N books and K shelves then for
a) The answer will be (N+(K-1))C(N) because the problem can be reduced to choosing N books from N+(K-1)) elements where K-1 is the Shelf divider count. Here only the number of ways the books can be placed is evaluated.
b) Here the above number is multiplied by N! as there are N! ways the books can be rearranged in each choice made above. Therefore the answer is (N+(K-1))C(N)*(N!).

answer Jun 12, 2017 by Tejas Naik



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