Processing math: 100%
Skip to main content
Library homepage
 

Text Color

Text Size

 

Margin Size

 

Font Type

Enable Dyslexic Font
Mathematics LibreTexts

10: Other Basic Counting Techniques

( \newcommand{\kernel}{\mathrm{null}\,}\)

There are two other elementary techniques that are surprisingly useful even in quite difficult counting problems. We will wrap up our exploration of enumeration by discussing these techniques.

  • 10.1: The Pigeonhole Principle
    The Pigeonhole Principle is a technique that you can apply when you are faced with items chosen from a number of different categories of items, and you want to know whether or not some of them must come from the same category, without looking at all of the items.
  • 10.2: Inclusion-Exclusion
    We could draw a very basic Venn diagram showing the kinds of trees that are growing at the various houses on my street. Naively, you might think that adding these together would give us the total number of houses with trees. However, in order to work out the number of houses that have trees, we must add the number that have deciduous trees to the number that have evergreen trees and then subtract the number that have both kinds of trees. This is the idea of “inclusion-exclusion.”
  • 10.3: Summary
    This page contains the summary of the topics covered in Chapter 10.


This page titled 10: Other Basic Counting Techniques is shared under a CC BY-NC-SA license and was authored, remixed, and/or curated by Joy Morris.

  • Was this article helpful?

Support Center

How can we help?