Problem:
Rabbits Peter and Pauline have three offspring-Flopsie, Mopsie, and Cottontail. These five rabbits are to be distributed to four different pet stores so that no store gets both a parent and a child. It is not required that every store gets a rabbit. In how many different ways can this be done?
Answer Choices:
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B.
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E.
Solution:
There are two cases. If Peter and Pauline are given to the same pet store, then there are 4 ways to choose that store. Each of the children must then be assigned to one of the other three stores, and this can be done in ways. Therefore there are possible assignments in this case. If Peter and Pauline are given to different stores, then there are ways to choose those stores. In this case, each of the children must be assigned to one of the other two stores, and this can be done in ways. Therefore there are possible assignments in this case. The total number of assignments is .
The problems on this page are the property of the MAA's American Mathematics Competitions