Question

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. \(\frac114\)
• B. \(\frac17\)
• C. \(\frac27\)
• D. \(\frac37\)

Hint:

When a question specifies “exactly” some category counts, multiply the combinations for each category rather than using permutations.

Answer 1

The Correct Option is D

Total employees = 3 men + 5 women = 8.
We select 4 employees, with exactly 2 women.
Number of ways to choose 2 women from 5: \(\binom52 = 10\).
Number of ways to choose 2 men from 3: \(\binom32 = 3\).
Thus, number of favorable ways: \(10 \times 3 = 30\).
Total number of ways to choose any 4 employees from 8: \(\binom84 = 70\).
Probability:
\[ P = \frac\textFavorable outcomes\textTotal outcomes = \frac3070 = \frac37 \] Thus, the probability is \(\frac37\).