Nine students are split into three equal teams to develop reports on

Solution:

First, there are [9C3 x 6C3 x 3C3] / 3! = [(9 x 8 x 7) / (3 x 2) x (6 x 5 x 4)/(3 x 2) x 1] / 6 = [84 x 20] / 6 = 280 ways the split 9 people into 3 equal teams. (Notice that 9C3 is the number of ways the first team could be chosen, 6C3 the second, and 3C3 the third. But once 3 teams are chosen, it doesn’t matter how we arrange them, they are still the same 3 teams; therefore, we need to divide by 3!).

Second, for every set of 3 teams, there are 3! = 6 ways the 3 reports can be assigned to them. Therefore, there are a total of 280 x 6 = 1680 different assignments.

Alternate Solution:

For the team reporting on shortage of skilled labor, there are 9C3 = 9!/(3! * 6!) = 84 choices.

Assuming the team reporting on shortage of skilled labor is chosen, there are 6C3 = 6!/(3! * 3!) = 20 choices for the team reporting on violence in schools.

If the teams reporting on shortage of skilled labor and violence in schools are chosen, then the three remaining students must form the team reporting on low standardized test scores; thus there is only one choice for that team.

By the fundamental principle of counting, there are 84 x 20 = 1680 ways to choose the teams and assign to a problem.

Answer: B