JEE Mains · Maths · STD 11 - 14. probability
The probability, of forming a 12 persons committee from 4 engineers, 2 doctors and 10 professors containing at least 3 engineers and at least 1 doctor, is:
- A \(\frac{129}{182}\)
- B \(\frac{103}{182}\)
- C \(\frac{17}{26}\)
- D \(\frac{19}{26}\)
Answer & Solution
Correct Answer
(A) \(\frac{129}{182}\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & 3 \text { engineering }+1 \text { doctor }+8 \text { Prof } \rightarrow{ }^4 \mathrm{C}_3 \cdot{ }^2 \mathrm{C}_1 \cdot{ }^{10} \mathrm{C}_8 \\ & =360 \\ & 3 \text { engineering }+2 \text { doctors }+7 \text { Prof } \rightarrow{ }^4 \mathrm{C}_3 \cdot{ }^2…
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