A salesman packed 3 shirts and 6 ties With one shirt he coul

A salesman packed 3 shirts and 6 ties. With one shirt, he could wear all 6 ties. With another shirt, he could wear 5 ties. With the third shirt, he could wear only 3 ties. How many different combinations did he have?

Question options: 13,33,14,90

Solution

We cannot take product beacause choices are not independent, if we choose shirt-1, we can have 6 ties, or 6 different combinations, in case of shirt-2, we can have another 5 different combinations. In case of third shirt we have 3 more combinaitons. These are not independent, instead these are disjoint (only one combination can occur), so total combinations are 6 + 5 + 3 = 14