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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
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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
EAMCET
EAMCET 2011
A
$\frac{35}{76}$
B
$\frac{35}{38}$
C
$\frac{7}{76}$
D
$\frac{35}{72}$
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} $