What is the probability that the committee includes <strong>EXACTLY</strong> 3 gentlemen?
Consider the following for the two (02) items that follow :<br>A committee of 6 members is formed from a group of 7 gentlemen and 4 ladies.
- A. 10/33 ✓
- B. 30/77
- C. 100/231
- D. 5/11
Correct Answer: A. 10/33
Explanation
Total ways to form a committee of 6 from 11 people is \binom{11}{6} = 462. Ways to select exactly 3 gentlemen and 3 ladies is \binom{7}{3} \times \binom{4}{3} = 35 \times 4 = 140. Probability = \frac{140}{462} = \frac{10}{33}.
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