Difference between revisions of "Overcounting"
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| − | + | Strategic '''overcounting''' is the process of counting more than desired and then systematically "correcting" for overcounted elements by removing them from the total count via subtraction or division. The idea of strategic overcounting is fundamental to [[combinatorics]] and plays a role in incredibly important counting tools such as [[combinations]] and the [[Principle of Inclusion-Exclusion]]. | |
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| − | == | + | ==Related Videos== |
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| − | + | * [http://www.artofproblemsolving.com/Videos/external.php?video_id=59 (Counting the Number of Arrangements of Letters in a Word)] | |
| + | * [http://www.artofproblemsolving.com/Videos/external.php?video_id=60 (Counting pairs)] | ||
| + | * [http://www.artofproblemsolving.com/Videos/external.php?video_id=57 (Counting Objects in a Circle Part 1)] | ||
| + | * [http://www.artofproblemsolving.com/Videos/external.php?video_id=61 (Counting Objects in a Circle Part 2)] | ||
| + | == More Examples == | ||
| + | |||
| + | * [[2004 AIME I Problems/Problem 3|AIME 2004I/3]] | ||
| + | |||
| + | ==Introductory Problems== | ||
| + | *How many different words can be formed with the letters <math>AAAABBCCDDDPPP</math>?(Not necessarily meaningful words) | ||
| + | |||
| + | == See also == | ||
| + | * [[Casework]] | ||
| + | * [[Complementary counting]] | ||
| + | * [[Constructive counting]] | ||
| + | |||
| + | {{stub}} | ||
| + | [[Category:Definition]] | ||
| + | [[Category:Combinatorics]] | ||
Latest revision as of 22:23, 22 July 2025
Strategic overcounting is the process of counting more than desired and then systematically "correcting" for overcounted elements by removing them from the total count via subtraction or division. The idea of strategic overcounting is fundamental to combinatorics and plays a role in incredibly important counting tools such as combinations and the Principle of Inclusion-Exclusion.
Related Videos
- (Counting the Number of Arrangements of Letters in a Word)
- (Counting pairs)
- (Counting Objects in a Circle Part 1)
- (Counting Objects in a Circle Part 2)
More Examples
Introductory Problems
- How many different words can be formed with the letters
?(Not necessarily meaningful words)
?(Not necessarily meaningful words)See also
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