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?

Number of ways of picking teams such that each gender remains in the same group is :
(10C5)(5C5)(10C5)(5C5)

Total number of ways of picking 4 groups of 5 is :
(20C5)(15C5)(10C5)(5C5)

So, probability becomes :

(10C5)(5C5)(10C5)(5C5) divided by (20C5)(15C5)(10C5)(5C5)

63504 / 11732745024

0.0000054125441122 ---> ANSWER