Question

4. A committee of 5 is formed by drawing lots from 8 boys and 6 girls. Find the probability that 

the committee will consist of 2 boys and 3 girls.

Answer 1

$$P(2\ boys\ and\ 3\ girls)=\dfrac{\dbinom{8}{2}\dbinom{6}{3}}{\dbinom{8+6}{5}}$$

$$=\dfrac{28(20)}{2002}=\dfrac{40}{143}\approx0.27972$$