The science club has 25 members: 10 boys and 15 girls. A 5-person committee is chosen at random. What is the probability that the committee has at least 1 boy and at least 1 girl?

Guest Jun 13, 2017

#1**+1 **

The total number of committees that can be formed = C(25,5) = 53130

And from this we just want to subtract all the commitees that can be formed solely of boys = C(10,5) = 252 and all the committees that can be formed solely of girls = C(15,5) = 3003

So.....the probability of a committee with at least one boy and one girl =

[ 53130 - 252 - 3003] / 53130 = .9387 = 93.87%

CPhill
Jun 13, 2017

#1**+1 **

Best Answer

The total number of committees that can be formed = C(25,5) = 53130

And from this we just want to subtract all the commitees that can be formed solely of boys = C(10,5) = 252 and all the committees that can be formed solely of girls = C(15,5) = 3003

So.....the probability of a committee with at least one boy and one girl =

[ 53130 - 252 - 3003] / 53130 = .9387 = 93.87%

CPhill
Jun 13, 2017