Probability distribution of people

Question

There is have a group of 50 people where 30 are men and 20 are women and they are being separated into two equal classes of 25 people, what is the probability that any of the two classes will have 15 men and 10 women? Could you please help me solve this? I've been on this for a while now, I've tried applying Bernoulli distribution but I seem to make mistake I don't see.

Answer 1

There are $\binom{50}{25}$ ways to choose $25$ people. There are $\binom{30}{15}$ ways to choose $15$ men, and $\binom{20}{10}$ ways to choose $10$ men, so $\binom{30}{15}\binom{20}{10}$ solutions exist, and a random choice has probability$$\frac{\binom{30}{15}\binom{20}{10}}{\binom{50}{25}}\approx0.227$$of meeting the condition.