alimad wrote:
A small company employs 3 men and 5 women. If a team of 4 employees is to be randomly selected to organize the company retreat, what is the probability that the team will have exactly 2 women?
A. 1/14
B. 1/7
C. 2/7
D. 3/7
E. 1/2
We need to determine the probability that when 4 employees are selected from 3 men and 5 women, 2 women and 2 men will be selected.
Let’s determine the number of ways to select the 2 women and 2 men.
Number of ways to select 2 women:
5C2 = (5 x 4)/2! = 10
Number of ways to select 2 men:
3C2 = (3 x 2)/2! = 3
Thus, 2 men and 2 women can be selected in 10 x 3 = 30 ways.
Finally, we can determine the number of ways to select 4 people from 8.
8C4 = 8! / [4! x (8-4)!] = (8x 7 x 6 x 5)/4! = (8 x 7 x 6 x 5)/(4 x 3 x 2) = 7 x 2 x 5 = 70
Thus, the probability is 30/70 = 3/7.
Answer: D
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