Q220 / 270 · NDA 2020 · Mathematics
A committee of 3 is to be formed from a group of 2 boys and 2 girls. What is the probability that the committee consists of 2 boys and 1 girl?
- A$\frac{2}{3}$
- B$\frac{1}{4}$
- C$\frac{3}{4}$
- Correct answerD$\frac{1}{2}$
Solution
Number of ways of selecting 2 boys out of 2 boys $={ }^2 C_2=1$.
Number of ways of selecting 1 girl out of 2 girls $={ }^2 C_1=2$.
Number of ways of selecting 3 out of 4 persons $={ }^4 C_3=4$.
$\therefore$ Required probability $=\frac{{ }^2 C_1 \times{ }^2 C_2}{{ }^4 C_3}=\frac{2 \times 1}{4}=\frac{1}{2}$.
Hence, the correct answer is option: 'D'.