Discrete Mathematics
# Combinations

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.

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