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  • From a group of 10 persons consisting of 5 lawyers, 3 doctors and 2 engineers, four persons are selected at random. The probability that the selection contains at least one of each category is<

From a group of 10 persons consisting of 5 lawyers, 3 doctors and 2 engineers, four persons are selected at random. The probability that the selection contains at least one of each category is

Option: 1

\frac{1}{2}


Option: 2

\frac{1}{3}


Option: 3

\frac{2}{3}


Option: 4

None of these


Answers (1)

best_answer

\begin{aligned} & \mathrm{n(S)={ }^{10} C_4=210} \\ \\& \mathrm{n(E)={ }^5 C_2 \times{ }^3 C_1 \times{ }^2 C_1+{ }^5 C_1 \times{ }^3 C_2 \times{ }^2 C_1+{ }^5 C_1 \times{ }^3 C_1 \times{ }^2 C_2=105} \\ \\& \mathrm{\therefore \quad P(E)=\frac{105}{210}=\frac{1}{2}} . \end{aligned}

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Irshad Anwar

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