Difference between revisions of "1993 AIME Problems/Problem 8"
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Revision as of 18:25, 4 July 2013
Problem
Let 
be a set with six elements. In how many different ways can one select two not necessarily distinct subsets of so that the union of the two subsets is ? The order of selection does not matter; for example, the pair of subsets 
, 
represents the same selection as the pair , .
Solution
Call the two subsets 
and 
. For each of the elements in 
, we can assign it to either , , or both. This gives us 
possible methods of selection. However, because the order of the subsets does not matter, each possible selection is double counted, except the case where both and contain all 
elements of . So our final answer is then 
See also
| 1993 AIME (Problems • Answer Key • Resources) | ||
| Preceded by Problem 7 |
Followed by Problem 9 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
| All AIME Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
