Question

For a quiz competition, a group of 3 students is selected randomly from a class consisting of 5 boys and 5 girls. What is the probability that one boy and two girls are selected?

• A. $\frac{2}{5}$
• B. $\frac{7}{13}$
• C. $\frac{2}{3}$
• D. $\frac{5}{12}$

Answer 1

The correct option is D $\frac{5}{12}$

Number of ways in which we can pick r objects from n objects (when the order is not important)
$={}^n{C}_r=\frac{n!}{(n-r)!r!}$

Number of ways in which group of 3 that can be formed from 5 boys and 5 girls
$={}^{10}{C}_3=\frac{10!}{7!3!}=120$

Number of ways of selecting one boy and two girls = Number of ways of selecting one boy from 5 boys $\times$ Number of ways of selecting two girls from 5 girls
$={}^5{C}_1\times {}^5{C}_2=5\times 10=50$

Probability that one boy and two girls are selected $=\frac{50}{120}=\frac{5}{12}$