your are teaching a 5th grade class with 13 boys and 17 girls. You need to choose 6 of your students to participate in your school's spelling bee. all participants are considered equal in standing.
A) how many ways can you choose your team?
b) what is the probability that the team you chose in part a consists of only girls?
C) "" ... only boys?
d) how many ways could you choose a team that consists of exactly 4 boys and two girls?

Question

your are teaching a 5th grade class with 13 boys and 17 girls. You need to choose 6 of your students to participate in your school's spelling bee. all participants are considered equal in standing.
A) how many ways can you choose your team?
b) what is the probability that the team you chose in part a consists of only girls?
C) "" ... only boys?
d) how many ways could you choose a team that consists of exactly 4 boys and two girls?

kropot72 · Answer

A) There are 30C6 ways of choosing the team.
$$30C6=\frac{30!}{6!24!}$$

anonymous · Answer

Find attached an image file with solution. You really just need to know Hypergeometric Distribution

kropot72 · Answer

B) The probability of choosing only girls is:
$$P(only\ girls)=\frac{17}{30}\times \frac{16}{29}\times \frac{15}{28}\times \frac{14}{27}\times \frac{13}{26}\times \frac{12}{25}$$

anonymous · Answer

Thank you all!! ^^

kropot72 · Answer

You're welcome :)