The urn contains 10 white and 6 black balls. Find the probability that 3 balls drawn at random

The urn contains 10 white and 6 black balls. Find the probability that 3 balls drawn at random one after the other turn out to be black?

You need to find how many ways there are to get 3 black balls out of the total. After that, find the number of ways to get any 3 balls in principle and divide the first by the second.

We find the first using the formula and combinatorics C:

C = 6! / (3! * (6 – 3)!) = (3! * 4 * 5 * 6) / (1 * 2 * 3 * 3!) = 4 * 5 = 20 (options for how to get 3 black balls).

Now we find the number of opportunities to get just three balls:

C = 16! / (3! * (16 – 3)!) = (13! * 14 * 15 * 16) / (1 * 2 * 3 * 13!) = 35 * 16 = 560 (just get three balls for variations).

The probability of getting three black balls out of the total:

20/560 = 2/56 = 1/28.

Answer: 1/28.