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
Solution
<p>$$\begin{array}{lll}
3 E, & 1 D, & 8 P \\
3 E, & 2 D, & 7 P \\
4 E, & 1 D, & 7 P \\
4 E, & 2 D, & 6 P
\end{array}$$</p>
<p>$$\begin{aligned}
& P=\frac{{ }^4 C_3 \cdot{ }^2 C_1 \cdot{ }^{10} C_8+{ }^4 C_3 \cdot{ }^2 C_2 \cdot{ }^{10} C_7+{ }^4 C_4 \cdot{ }^2 C_1 \cdot{ }^{10} C_7+{ }^4 C_4 \cdot{ }^2 C_2 \cdot{ }^{10} C_6}{{ }^{10} C_{12}} \\
& =\frac{129}{182}
\end{aligned}$$</p>
About this question
Subject: Mathematics · Chapter: Probability · Topic: Classical and Axiomatic Probability
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