Probability
Classical Probability
Grade 12
Question:
<p>From a group of 4 men and 3 women, a committee of 3 is chosen at random. The probability that the committee has exactly 2 men and 1 woman is</p>
<p>\(\dfrac{18}{35}\)</p>
<p>\(\dfrac{12}{35}\)</p>
<p>\(\dfrac{3}{7}\)</p>
<p>\(\dfrac{6}{35}\)</p>
Step-by-Step Solution
Key Concept: P(2M,1W) = C(4,2) \times C(3,1)/C(7,3).
<p>$P(2M, 1W) = \dfrac{\binom{4}{2} \times \binom{3}{1}}{\binom{7}{3}} = \dfrac{6 \times 3}{35} = \dfrac{18}{35}$</p>
Correct Answer: A