Difference between revisions of "Principle of Inclusion-Exclusion"
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2011 AMC 8 Problems/Problem 6 | 2011 AMC 8 Problems/Problem 6 | ||
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Revision as of 12:49, 19 July 2017
The Principle of Inclusion-Exclusion (abbreviated PIE) provides an organized method/formula to find the number of elements in the union of a given group of sets, the size of each set, and the size of all possible intersections among the sets.
Remarks
Sometimes it is also useful to know that, if you take into account only the first sums on the right, then you will get an overestimate if
is odd and an underestimate if
is even.
So,
and so on.
Examples
2002 AIME I Problems/Problem 1 http://artofproblemsolving.com/wiki/index.php?title=2002_AIME_I_Problems/Problem_1#Problem
2011 AMC 8 Problems/Problem 6 https://artofproblemsolving.com/wiki/index.php?title=2011_AMC_8_Problems/Problem_6