Inviting four of ten friends to dinner

Question

You want to invite 4 friends to dinner and have 10 friends to choose from. A guest list is just a set of people, so order does not matter. How many different guest lists of 4 are possible?

Accepted Answer

Choosing 4 from 10 with order ignored is the combination \binom{10}{4}: \binom{10}{4} = \frac{10 	imes 9 	imes 8 	imes 7}{4!} = \frac{5040}{24} = 210. The numerator counts ordered lists of 4 guests; dividing by 4! = 24 collapses the 24 orderings of each guest list into one. Takeaway. An unordered guest list is a combination: \binom{10}{4} = 210.

Inviting four of ten friends to dinner

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