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Question
A committee of 5 is to be chosen from a group of 9 people. The probability that a certain married couple will either serve together or not at all is
🎥 Video solution / Text Solution of this question is given below:
Total people: 9
Married couple: 2 specific people among them
Total ways to choose 5 people from 9:
\text{Total} = \binom{9}{5} = 126
✅ Case 1: Both are selected
We fix the married couple (2 people), then choose 3 more from remaining 7:
\binom{7}{3} = 35
✅ Case 2: Both are NOT selected
We remove both from the pool, then choose 5 from remaining 7:
\binom{7}{5} = \binom{7}{2} = 21
✅ Favorable outcomes:
\text{Favorable} = 35 + 21 = 56
✅ Probability:
\text{Required Probability} = \frac{56}{126} = \frac{28}{63} = \frac{4}{9}
✅ Final Answer: \boxed{\dfrac{4}{9}}
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