There are 6 white and 4 black balls in the urn. What is the probability that among 5

There are 6 white and 4 black balls in the urn. What is the probability that among 5 balls taken out of the urn at random there will be 3 white and 2 black?

Let’s count the number of balls – 10 balls in total.

The outcome is the choice of any 5 balls.

The number of all outcomes is C5 10 = 10! / (5! * 5!) = 3628800/120 * 120 = 3628800/14400 = 252.

Favorable outcome – choice of 3 white balls and 2 black ones.

3 white balls out of 6 can be chosen in C36 ways. And you can choose 2 black balls out of 4 in C24 ways.

The number of favorable outcomes is equal to the product

C36 * C24 = 6! / (3! * 3!) * 4! / (2! * 2!) = 720 / (6 * 6) * 24 / (2 * 2) = 720/36 * 24/4 = 20 * 6 = 120.

P = 120/252 ≈ 0.476.