a) Panama Canal is a notorious bottleneck in international shipping. A large modern ship takes up the entire canal, so they have to go one at a time. You have five ships lined up at the entrance, and every hour of wait inflicts costs on the shipping companies. Find the number of ways to let through three ships out of five (one at a time). Show calculation. Explain why you went with your formula, rather than the alternative.

(b) A company has two identical openings and is choosing among six applicants. Find how many ways there are to fill two positions with six candidates. Show calculation. Explain why you went with your formula, rather than the alternative.

(c) You are one of the six applicants. List all the combinations that allow you to land one of the jobs. Then, using the classical definition of probability and your answer from (b), calculate the probability of you getting one of the two jobs.