Solve the problem.
-How many ways are there to choose a soccer team consisting of 3 forwards, 4 midfield players, and 3 defensive players, if the players are chosen from 8 forwards, 10 midfield players, and 8 defensive players?
A) 322
B) 568,995,840
C) 658,560
D) 5,311,735

Question

Quizplus · Accepted Answer

The number of ways to choose the soccer team can be calculated using combinations since the order in which the players are chosen does not matter. For forwards, there are $C(8,3) = \frac{8!}{3!(8-3)!} = 56$ ways. For midfield players, $C(10,4) = \frac{10!}{4!(10-4)!} = 210$ ways. For defensive players, $C(8,3) = \frac{8!}{3!(8-3)!} = 56$ ways. The total number of ways to choose the team is the product of these, which is $56 \times 210 \times 56 = 658,560$.

Solve the Problem. -How Many Ways Are There to Choose a Soccer Team