Question

A class consist of $10$ boys and $8$ girls. Three students are selected at random. What is the probability that the selected group has $1$ boy and $2$ girls?

• A. $\frac{34}{103}$
• B. $\frac{35}{102}$
• C. $\frac{36}{107}$
• D. None of these

Answer 1

The correct option is B $\frac{35}{102}$

Given

Boys $=10$

Girls $=8$

Total no. of students $=18$

Total no. of events ${=}^{18}{C}_3$

The probability that $1$ boy and $2$ girls

${=}^{10}{C}_1{\times }^8{C}_2$

$\therefore$ probability of $1$ boy and $2$ girls

$=\frac{{}^{10}{C}_1{\times }^8{C}_2}{{}^{18}{C}_2}$

${}^{10}{C}_1=\frac{10!}{9!1!}=\frac{10\times 9!}{9!}$

${}^8{C}_2=\frac{8!}{6!2!}=\frac{8\times 7\times 6!}{6!\times 2\times 1}=28$

${}^{18}{C}_3=\frac{18!}{15!3!}=\frac{18\times 17\times 16\times 15!}{15!\times 3\times 2}=816$

$=\frac{10\times 28}{816}$

$=\frac{280}{816}$

$=\frac{35}{102}$

The given answer is correct.