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 6 forwards, 6 midfield players, and 9 defensive players?
A)21,772,800
B)25,200
C)119
D)352,716

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, we choose 3 out of 6, for midfield players, we choose 4 out of 6, and for defensive players, we choose 3 out of 9. The total number of ways is the product of these combinations: $ \binom{6}{3} \times \binom{6}{4} \times \binom{9}{3} = 20 \times 15 \times 84 = 25,200$.

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