Math CentralQuandaries & Queries


Question from Gil, a parent:

A school cafeteria offers 2 main entrees, 3 fruits, 4 vegetables, and 3 drinks. If a plate consists of 1 entree, 2 vegetables, 1 fruit, and 1 drink, how many different plates can a cafeteria manager make? Please explain how you derived at answer. Thank you

Hi Gil,

Think about walking down the cafeteria offerings and selecting your meal. At the entree station there are 2 items so you have 2 choices of which to select. Next you come to the fruit station. There are 3 fruits available and regardless of the entree you selected you can choose one of the fruits. Thus at this point you have $2 \times 3$ possible partial meals. Next comes the drinks station. Again there are 3 possible selection and regardless of what you have on your tray so far you have three choices of a drink and hence there are $2 \times 3 \times 3$ possible partial meals at this point.

Finally you come to the vegetable station. This time there are 4 vegetables available and you can choose any 2 of them. How many ways are there of choosing 2 things from 4 things? Multiply this number of choices by the number of possible partial meals you have at this point to obtain the number of possible meal trays.


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