In the box there are 15 parts, including 8 painted. The random collector retrieves three parts. Find the likelihood

In the box there are 15 parts, including 8 painted. The random collector retrieves three parts. Find the likelihood that the extracted parts turn out to be colored

Decision. Event A = {three colored parts removed}.
The total number of all possible elementary outcomes of the test is equal to the number of ways in which 3 parts can be extracted from 15:
n = C15 3 = 15! / 3! (15-3)! = 15! / (3! * 12!) = 13 * 7 * 5 = 455.
The number of favorable outcomes is equal to the number of ways in which you can extract 3 parts from 8 painted:
m = C8 3 = 8! / 3! (8-3)! = 8! / (3! * 5!) = 7 * 8 = 56.
The probability of event A is found as the ratio: P (A) = m / n = 56 / 455≈0.12

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