A man has a wardrobe consisting of: 5 sports coats, 5 pair of pants, 6 shirts, and 3 ties. How many combinations of these items can he wear, assuming that he must wear pants and a shirt?

Answer 1

SC = sport coat, P = pants, S = shirt, T = tie

There are multiple combinations of general outfit he could wear. Given that he has to choose P and S, there is the option to wear or not wear T or SC. The first option would be to wear all four components which would be SC x P x S x T combinations, or 450. There is the option to ignore T, and then you have SC x P x S which is 150. Same thing with ignoring SC instead of T, P x S x T = 90. Or he could ignore SC and T which is P x S = 30. You would just add all these values together to get the total number of combinations.

450 + 150 + 90 + 30 = 720