misstokyo wrote:In how many ways can a comittee of five be chosen out of 15 people, 7 of which are males and 8 of which are females, if one male and one female are to be included in each selection?

In how many ways can you choose the one required male? In how many ways can you choose the one required female? In how many ways can you choose the remaining three members? Multiplying, what value do you get?

misstokyo wrote:A shipment of 14 personal computers contains 4 defective units. In how many ways can a company purchase 5 of these units and receive at least 2 of the defective units?

To receive "at least two", you will receive two or three or four. The opposite possibility is receiving zero or one. So one method would be:

In how many ways can you chose none of the defective units from the four available? In how many ways can you choose the remaining five units from the remaining ten?

In how many ways can you choose one of the defective units from the four available? In how many ways can you choose the remaining four units from the remaining ten?

Subtract these values from the total number of ways to choose five of fourteen.