Q95 / 160 · AP EAMCET 2011 · Mathematics

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

  • Correct answer
    A
    $\frac{35}{76}$
  • B
    $\frac{35}{38}$
  • C
    $\frac{7}{76}$
  • D
    $\frac{35}{72}$

Solution

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

Hence, the correct answer is option: 'A'.

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