Problem:
Tyler has entered a buffet line in which he chooses one kind of meat, two different vegetables and one dessert. If the order of food items is not important, how many different meals might he choose?
Meat: beef, chicken, pork
Vegetables: baked beans, corn, potatoes, tomatoes
Dessert: brownies, chocolate cake, chocolate pudding, ice cream
Answer Choices:
A.
B.
C.
D.
E.
Solution:
There are choices for the meat and for dessert.
There are ways to choose the two vegetables. The first vegetable may be chosen in ways and the second in ways. This would seem to make ways, but since the order is not important the must be divided by . Otherwise, for example, both tomatoes/corn and corn/tomatoes would be included. The choices are beans/corn, beans/potatoes, beans/tomatoes, corn/potatoes, corn/tomatoes and potatoes/tomatoes.
The answer is .
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions