Permutations & Combinations

An election ballot asks voters to select three city commissioners from a group of six candidates. In how many ways can this be done? (The order they are voted doesn't matter.)

The ski club with ten members is to choose three officers for captain, co-captain and secretary. How many ways can those offices be filled?

The student body of 30 students wants to elect a president, vice president, secretary, and treasurer.

A group of 14 people need to take an elevator to the top floor. If they can go in groups of 7, how many different ways can they go up?

The five starters on a 12 person basketball team.

A group of 20 people are going to run a race. The top 4 finishers advance to the finals.

Selecting the batting order on a 9 person baseball team.

Five students from 90 will be selected to help count ballots. How many groups of 5 students could be selected to count ballots?

You are watching a horse race with 8 horses. How many ways can you pick the first, second, and third place?