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.