A committee of 5 is to be chosen from a group of 9 people. The probability th...

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Question Id : 11635 | Context :NIMCET 2024

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:

Married couple: 2 specific people among them

Total ways to choose 5 people from 9:

$\text{Total} = \binom{9}{5} = 126$

We fix the married couple (2 people), then choose 3 more from remaining 7:

$\binom{7}{3} = 35$

We remove both from the pool, then choose 5 from remaining 7:

$\binom{7}{5} = \binom{7}{2} = 21$

$\text{Favorable} = 35 + 21 = 56$

$\text{Required Probability} = \frac{56}{126} = \frac{28}{63} = \frac{4}{9}$

✅ Final Answer: $\boxed{\dfrac{4}{9}}$

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