I have come across a question on joint and conditional probability. In a shipment of 20 packages, 7 packages are damaged. The packages are randomly inspected, one at a time, without replacement, until the fourth damaged package is discovered. Calculate the probability that exactly 12 packages are inspected.
Part of Solution: The requested probability can be determined as P(3 of first 11 damaged)P(12th is damaged | 3 of first 11 damaged).
I don't know how they came up with this part of the solution shown above, can someone explain how they got that?