Probability

# 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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