Packing five of eight books for a trip

Question

You own 8 books and will pack exactly 5 of them for a trip. Only which books you bring matters, not the order they go in the bag. How many different sets of 5 books can you pack?

Accepted Answer

This is choosing 5 items from 8 with order irrelevant, so it is the combination \binom{8}{5}: \binom{8}{5} = \frac{8 	imes 7 	imes 6 	imes 5 	imes 4}{5!} = \frac{6720}{120} = 56. A shortcut: picking 5 to bring is the same as picking the 3 to leave behind, so \binom{8}{5} = \binom{8}{3} = \dfrac{8 	imes 7 	imes 6}{6} = 56, which confirms the answer. Takeaway. Selecting a subset with order ignored is a combination. Here \binom{8}{5} = \binom{8}{3} = 56.

Packing five of eight books for a trip

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