Question

From a group of $8$ boys and $3$ girls, a commitee of $5$ members to be formed. Find the probability that $2$ particular girls are included in the commitee is

• A. $\frac{4}{11}$
• B. $\frac{2}{11}$
• C. $\frac{6}{11}$
• D. $\frac{8}{11}$

Answer 1

The correct option is B $\frac{2}{11}$

$8$ boys ; $3$ girls

commitee : $2$ particular girls $+3$ members

No. of ways to select 2 particular girls ${=}^2{C}_2$

No. of ways to select 3 members from $(8+3-2)=9$ members

${=}^9{C}_3$

$\therefore$ Probability $=\frac{{}^2{C}_2{.}^9{C}_3}{{}^{11}{C}_5}=\frac{84}{462}=\frac{2}{11}$