Difference between revisions of "2021 AIME II Problems/Problem 6"
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==Problem== | ==Problem== | ||
| − | + | For any finite set <math>S</math>, let <math>|S|</math> denote the number of elements in <math>S</math>. FInd the number of ordered pairs <math>(A,B)</math> such that <math>A</math> and <math>B</math> are (not necessarily distinct) subsets of <math>\{1,2,3,4,5\}</math> that satisfy<cmath>|A| \cdot |B| = |A \cap B| \cdot |A \cup B|</cmath> | |
| + | |||
==Solution== | ==Solution== | ||
We can't have a solution without a problem. | We can't have a solution without a problem. | ||
Revision as of 14:17, 22 March 2021
Problem
For any finite set 
, let 
denote the number of elements in . FInd the number of ordered pairs 
such that 
and 
are (not necessarily distinct) subsets of 
that satisfy![\[|A| \cdot |B| = |A \cap B| \cdot |A \cup B|\]](http://latex.artofproblemsolving.com/a/8/c/a8c5056f13bbfd71412164ca53b71c92395e5812.png)
Solution
We can't have a solution without a problem.
See also
| 2021 AIME II (Problems • Answer Key • Resources) | ||
| Preceded by Problem 5 |
Followed by Problem 7 | |
| 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. 
