# Difference between revisions of "Principle of Inclusion-Exclusion"

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The '''Principle of Inclusion-Exclusion''' (abbreviated PIE) provides an organized method/formula to find the number of [[element]]s in the [[union]] of a given group of [[set]]s, the size of each set, and the size of all possible [[intersection]]s among the sets. | The '''Principle of Inclusion-Exclusion''' (abbreviated PIE) provides an organized method/formula to find the number of [[element]]s in the [[union]] of a given group of [[set]]s, the size of each set, and the size of all possible [[intersection]]s among the sets. | ||

− | + | == 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 | ||

+ | |||

+ | 2017 AMC 10B Problems/Problem 13 | ||

+ | https://artofproblemsolving.com/wiki/index.php?title=2017_AMC_10B_Problems/Problem_13 | ||

+ | |||

+ | 2005 AMC 12A Problems/Problem 18 | ||

+ | https://artofproblemsolving.com/wiki/index.php/2005_AMC_12A_Problems/Problem_18 | ||

== See also == | == See also == |

## Revision as of 19:42, 26 October 2020

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.

## 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

2017 AMC 10B Problems/Problem 13 https://artofproblemsolving.com/wiki/index.php?title=2017_AMC_10B_Problems/Problem_13

2005 AMC 12A Problems/Problem 18 https://artofproblemsolving.com/wiki/index.php/2005_AMC_12A_Problems/Problem_18