From a group of \(6\) boys and \(6\) girls a volleyball team of \(6\) players is to be selected. What is the probability

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From a group of \(6\) boys and \(6\) girls a volleyball team of \(6\) players is to be selected. What is the probability that the team consists of \(4\) boys and \(2\) girls?

A. \(\dfrac{5}{33}\)
B. \(\dfrac{225}{308}\)
C. \(\dfrac{5}{22}\)
D. \(\dfrac{225}{311}\)
E. \(\dfrac{75}{308}\)

OA E

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To find the probability that the volleyball team consists of 4 boys and 2 girls, we need to consider the total number of ways to select 4 boys from the group of 6 boys and 2 girls from the group of 6 girls, divided by the total number of ways to select 6 players from the combined group of boys and girls.

Total number of ways to select 4 boys from group of 6 = 6C4 = 15
Total number of ways to select 2 girls from group of 6 = 6C2 = 15
Total number of ways to select 6 players from group of 12 = 12C6 = 924

The probability that the team consists of 4 boys AND 2 girls
= (15 x 15) / 924
= 75/308
The correct answer is E

Bernard Baah
MS '05, Stanford
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