THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING:
In an office of 18 people,there are 7 men and 11 women.A subcommittee of four people will be formed from this group.
-What is the probability that the subcommittee contains two men and two women?
A)0.377
B)0.522
C)0.261
D)0.755

Question

Quizplus · Accepted Answer

Total number of ways to select a subcommittee of 4 people from 18 people = 18C4 = 3060
Number of ways to select 2 men out of 7 men = 7C2 = 21
Number of ways to select 2 women out of 11 women = 11C2 = 55
So, the number of ways to select 2 men and 2 women = 21 * 55 = 1155
Therefore, the probability of selecting a subcommittee with 2 men and 2 women = 1155/3060 = 0.377, which is option A.