An office furniture manufacturer makes filing cabinets. It offers customers 2 choices for the base and 4 choices for the top, and 5 different heights. A customer may choose any combination of the 5 different-sized modules so that the finished filing cabinet has a base, a top, and 1, 2, 3, 4, 5, or 6 storage modules.
a) How many choices does the customer have if the completed filing cabinet has 4 storage modules, a top and a base? The order in which the 4 storage modules are stacked is irrelevant.
b) The manufacturer would like to know the number of different files that are possible - selecting 1 of the 2 bases, 1 of the 4 tops and then either 1 or 2 or 3 or 4 or 5 or 6 storage modules, selecting any combination of the 5 different sizes with the order of stacking irrelevant. What is the number of possibilities?
A nice probability problem which use the concepts of combination.