Problem:
Two subsets of the set are to be chosen so that their union is and their intersection contains exactly two elements. In how many ways can this be done, assuming that the order in which the subsets are chosen does not matter?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Let the two subsets be and . There are ways to choose the two elements common to and . There are then ways to assign the remaining three elements to or , so there are ordered pairs that meet the required conditions. However, the ordered pairs and represent the same pair of subsets, so the conditions can be met in ways.
The problems on this page are the property of the MAA's American Mathematics Competitions