# How many ways to divide 5 different books among 3 children so that each child gets at least one book?

How can you divide 5 different books among 3 children such that each child gets at least one book? (no book can be divided)

Some one please tell me how to solve this.

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Inclusion-exclusion principle –  Noturab Mar 31 '13 at 22:52

This is the number of onto functions from a $5$-element set to a $3$-element set. Here, principle of inclusion & exclusion is useful.

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I would use inclusion-exclusion. Count the total ways to distribute the books. Subtract three times the number of ways to give them to a specific pair. But you have subtracted the ways to gove them all to one child twice (paired once with each of the others) so add them in once.

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