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 committe is

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

Answer 1

Answer: (B)

$\frac{2}{11}$

Answer 2

Total number of ways $={ }^{8} C_{2}{ }^{3} C_{3}+{ }^{8} C_{3}{ }^{3} C_{2}+{ }^{8} C_{4}{ }^{3} C_{1}+{ }^{8} C_{5}{ }^{3} C_{0}$ $=28 \times 1+56 \times 3+70 \times 3+56 \times 1$ $=462$ Number of ways in which $2$ particular girls are included ${ }^{P} C_{3}=84$ $\therefore\,\,\,$Required probability $=\frac{84}{462}=\frac{2}{11}$