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Q. 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

EAMCETEAMCET 2011

Solution:

$\therefore $ 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} $