Problem:
Pat wants to buy four donuts from an ample supply of three types of donuts: glazed, chocolate, and powdered. How many different selections are possible?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
The number of possible selections is the number of solutions of the equation
where , and represent, respectively, the number of glazed, chocolate, and powdered donuts. The possible solutions to this equations are , , , , , , , , , , , , , and .
Code each selection as a sequence of four 's and two 's, where * represents a donut and each - denotes a "separator" between types of donuts. For example **__*__** represents two glazed donuts, one chocolate donut, and one powdered donut. From the six slots that can be occupied by a - or a *, we must choose two places for the -'s to determine a selection. Thus, there are selections.
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions