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AMC 12 Mock Exam 5 Problem 5

Problem 5 of 25

A smoothie bar offers 66 different fruits. Each smoothie is made from at least one and at most three different fruits, and two smoothies are considered the same if they use the same set of fruits. How many different smoothies can be made?

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Solution

A smoothie is a set of 11, 22, or 33 of the 66 fruits, so the count is (61)+(62)+(63)=6+15+20=41\binom61+\binom62+\binom63=6+15+20=\boxed{41}.

Tagged: combinations with a range of sizes