Advanced Counting Techniques CSC-2259 Discrete Structures Konstantin Busch - LSU1.
Counting Techniques
-
Upload
rooney-holmes -
Category
Documents
-
view
18 -
download
0
description
Transcript of Counting Techniques
![Page 1: Counting Techniques](https://reader036.fdocuments.net/reader036/viewer/2022072014/56812d88550346895d929c43/html5/thumbnails/1.jpg)
Counting Techniques
The Fundamental Rule of Counting (the mn Rule);
Permutations; andCombinations
![Page 2: Counting Techniques](https://reader036.fdocuments.net/reader036/viewer/2022072014/56812d88550346895d929c43/html5/thumbnails/2.jpg)
The Fundamental Rule of Counting
If event A can occur in m distinct ways and event B can occur in any of n distinct ways (regardless of how event A occurs), then event A and event B can occur in mn ways.
![Page 3: Counting Techniques](https://reader036.fdocuments.net/reader036/viewer/2022072014/56812d88550346895d929c43/html5/thumbnails/3.jpg)
Permutations
When different arrangements count as distinct outcomes but duplication of items is not allowed, then Permutations is the counting procedure for the arrangement of items.
If there are n items and each item can occur x different ways, then
Number of ways = Pnx = (n!) / (n - x)!
![Page 4: Counting Techniques](https://reader036.fdocuments.net/reader036/viewer/2022072014/56812d88550346895d929c43/html5/thumbnails/4.jpg)
Combinations
When different arrangements do not count as distinct outcomes and duplication of items is not allowed, then Combinations is the counting procedure for the arrangement of items.
If there are n items and each item can occur x different ways, then
Number of ways = Cnx = (n!) / x!(n - x)!