Question

A class has fifteen boys and five girls. Suppose three students are selected at random form class. The probability that there are two boys and one girl is

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

Answer 1

The correct option is A $\frac{35}{76}$

Given that the class has fifteen boys and five girls
Three students are selected at random
To find the Probability that there are two boys and one girl can be done as follows
Selection of $2$ boys from $15$ boys can be done in $(\frac{15}{2})$ ways $=105$
Similarly, Selection of $1$ girl from $5$ girls can be done in $(\frac{5}{1})$ ways $=5$
Selection of $3$ students from $20$ students can be done in $(\frac{20}{3})$ ways $=1140$
Hence, Required Probability
$=\frac{105\times 5}{1140}$
$=\frac{35}{76}$