A teacher randomly assigns the 20 students in her class to s

A teacher randomly assigns the 20 students in her class to study groups, each with 5 students. If there

are 10 boys and 10 girls, what is the probability that two of the study groups have all boys and two

have all girls?

Solution

Total possible outcomes = 20!/(5!)^4
Possible outcomes for all boys in 2 groups = (10 choose 5)*(5 choose 5) = (10 choose 5) = 252
P(all boys in 2 groups) = 252 / total possible outcomes = .000000021