There are 20 students in a club, 12 boys and 8 girls. If 5 members of the cub are chosen at random, what is the probability that in the group chosen there are exactly 2 boys?

Question

anonymous · Answer

Given: 

20 students in total
12 boys
8 girls

• If there is no any restrictions, there are $\sf  _{20}C_{5}$ ways that they can choose the members.

• 5 members are needed and there should be EXACTLY two boys in the club. This means we need three girls and 2 boys to complete the club. So $\sf   _{8}C_{3} \times   _{12}C_{2}$ will be the number of ways that exactly two boys will be included in the team.

Now, probability will be $\sf \Large \frac{\sf   _{8}C_{3} \times   _{12}C_{2}}{  _{20}C_{5}}$

anonymous · Answer

btw, welcome to openstudy @cjsyki

anonymous · Answer

thanks!