A committee of size five is selected from a group of ten clowns and twelve lion tamers. (a) How many di erent committees are possible? (b) How many committees are possible if there must be exactly two clowns on the committee? (c) How many committees are possible if lion tamers must outnumber clowns on the committee?

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a) = 22 choose 5 ???

first one is straightforward yes? no restrictions it is \[\dbinom{22}{5}\]

yup

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