Barbara is a research biologist for green carpet lawns. she is studying the effects of fertilizer type, temperature at time of application, and water treatment after application. she has three fertilizer types, two temperature zones, and five water treatments to test. determine the number of different lawn plots she needs in order to test each fertilizer type, temperature range, and water treatment configuration.

the university of montana ski team has ten entrants in a men's downhill ski event. the coach would like the first, second, and third places to go to the team members. in how many ways can the ten team entrants achieve first, second, and third places?

there are 15 qualified applicants for 4 trainee positions in a fast-food management program. how many different groups of trainees can be selected?