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Combinations without Repetition


A juggler has \(12\) different objects that she likes to juggle. How many different sets of \(5\) objects can she choose to juggle?

How many ways can three different appetizers be chosen from a menu that has 10 choices?

Sandy and Judy are planning a trip to California. If they want to visit exactly \(5\) cities among San Francisco, Berkeley, Napa, Monterey, and Santa Cruz, how many choices do they have for which \(5\) cities to visit?

Details and assumptions

The order in which they visit the cities does not matter.

The Maniacs track team has \(18\) athletes including Alice and Bob. How many ways are there to choose \(4\) out of the \(18\) athletes, such that both Alice and Bob are chosen?

Details and assumptions

The order of the chosen athletes does not matter.

Snow White needs to send 3 of the 7 dwarves to buy hay for feeding the horses. How many choices does Snow White have for which 3 dwarves she will send?


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