<p>6 married couples are together in a group of 12 people. If 4 people are selected at random, the probability that exactly one married couple is among the selected 4 is</p>
Step-by-Step Solution
Key Concept: Choose 1 couple from 6, then choose remaining 2 from the other 10 persons ensuring they don't form another couple.
<p>Total ways: $\binom{12}{4} = 495$.</p><p>Exactly 1 couple: Choose which couple $\binom{6}{1} = 6$. From remaining 10 persons (5 couples), choose 2 with no married pair: $\binom{10}{2} - \binom{5}{1} = 45 - 5 = 40$.</p><p>Favorable = $6 \times 40 = 240$.</p><p>$P = \dfrac{240}{495} = \dfrac{16}{33}$</p>
Correct Answer: A