Permutations and Combinations

Sarah and Joe are planning trips to three countries this year. There are 7 countries they would like to visit. One trip will be one week long, another two days, and the last one two weeks. How many possibilities are there for their vacation?

You are setting the combination on a three-digit lock. You want to use the numbers 123 but don't care what order they are in. How many possible combinations are there?

How many ways can a coach choose 3 players out of a team of 17 softball players to refill the water cooler?

How many ways can a club of 10 students elect a president, vice president, secretary, and treasurer?

How many ways can an employer fill four jobs: Computer Programmer, Software Tester, Manager, and Systems Engineer, if they have 15 applicants?

A group of 25 people are going to run a race. The top 8 finishers advance to the finals. How many different groups of 8 are possible?

How many ways can a teacher choose 5 students out of 13 to ride in a car instead of the van?

A group of 45 students are going to run a race. The top 3 runners earn gold, silver, and bronze medals. How many possibilities are there for these medals?