Problem 3. How many ways are there to select an 11-member soccer team and a 5-member basketball team from a class of 30 students if (1) nobody can be on both teams. (2) any number of students can be on both the teams. (3) at most one student can be on both the teams.

Suppose that Jeremy is a highschool science teacher and that he is dividing 16 students in his advanced chemistry class into four groups of four for a lab activity. Each of the four lab groups has been assigned its own task to complete for the activity, but the students are not assigned specific roles within the group. How many different ways can Jeremy assign his students to the four lab groups?

Consider a 6 vs 6 youth soccer team (i.e., teams field 6 players at once) with 9 players. (a) How many different combinations of players can the team field? (b) If the team has exactly one goalie (who has to play), how many different combinations of players can the team field? (c) If the team has exactly two goalie (exactly one of which has to play and the other cannot), how many different combinations of players can the team field?

2.) The BOS-14 is the new model of cars manufactured by NUC Motors. This model can be achieved in 2 body styles, 4 interior options and 7 different colors. The model can be achieved in automatic transmission as a manual. ER Auto wants to have a model of each of the options available to sell. How many BOS-14 models should you order?