A committee of three has to be chosen from a group of 4 men and 5 women. If the selection is made at randon, what is the probability that exactly two members are men?

Options

A. `(5)/(14)`
B. `(1)/(21)`
C. `(3)/(14)`
D. `(8)/(21)`

Answer

A

Explanation

`n(E) = ""^(4)C_(2) xx ""^(5)C_(1) = 6 xx 5 = 30`
`n(S) = ""^(9)C_(3) = 84`.
`therefore` Probability, `P(E) = (n(E))/(n(S)) = (30)/(84) = (5)/(14)`.