A football team consists of 20 freshmen and 20 sophomores, 12 juniors, and 5 seniors. Four players are selected at random to serve as captains. Find the probability that there
Are 2 sophomores and 2 freshmen.
A) $\approx 0.0914$
B) $ \approx 0.0005$
C) $\approx 0.2000$
D) $ \approx 0.3950$

Question

A football team consists of 20 freshmen and 20 sophomores, 12 juniors, and 5 seniors. Four players are selected at random to serve as captains. Find the probability that there
Are 2 sophomores and 2 freshmen. 
A) $\approx 0.0914$
B) $ \approx 0.0005$
C) $\approx 0.2000$
D) $ \approx 0.3950$

Quizplus · Accepted Answer

The total number of ways to select 4 players out of 57 is $C(57,4)$. The number of ways to select 2 sophomores out of 20 and 2 freshmen out of 20 is $C(20,2) \times C(20,2)$. The probability is therefore $\frac{C(20,2) \times C(20,2)}{C(57,4)} \approx 0.0914$.

A Football Team Consists of 20 Freshmen and 20 Sophomores ≈0.0914\approx 0.0914≈0.0914

A Football Team Consists of 20 Freshmen and 20 Sophomores $\approx 0.0914$