A class has fifteen boys and five girls. Suppose three students are selected at random from the class. The…

A class has fifteen boys and five girls. Suppose three students are selected at random from the class. The probability that there are two boys and one girl is
  1. $\frac{35}{76}$
  2. $\frac{35}{38}$
  3. $\frac{7}{76}$
  4. $\frac{35}{72}$

Solution

$\begin{aligned} \therefore \text { Required probability } & =\frac{{ }^{15} C_2 \times{ }^5 C_1}{{ }^{20} C_3} \\ & =\frac{15 \times 7 \times 5}{\frac{20 \times 19 \times 18}{3 \times 2}} \\ & =\frac{7 \times 25}{20 \times 19}=\frac{35}{76}\end{aligned}$

Asked in: AP EAMCET 2011

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