Question

There are $15$ boys and $10$ girls in a class. If three students are selected at random, then what is the probability that $1$ girl and $2$ boys are selected?

• A. $\frac{21}{46}$
• B. $\frac{25}{46}$
• C. $\frac{1}{2}$
• D. $\frac{19}{46}$

Answer 1

The correct option is A $\frac{21}{46}$

Number of boys $=15$
Number of girls $=10$
Total number of ways of selecting $3$ students from $25$ students $={}^{25}{C}_3$
Number of ways of selecting $1$ girl and $2$ boys $=$ selecting $2$ boys from $15$ boys and $1$ girl from $10$ girls
Number of ways in which this can be done $={}^{15}{C}_2\times {}^{10}{C}_1$
$\therefore$ Required probability $=\frac{{}^{15}{C}_2\times {}^{10}{C}_1}{{}^{25}{C}_3}=\frac{21}{46}$