42 lines
2.0 KiB
Markdown
42 lines
2.0 KiB
Markdown
|
---
|
||
|
|
title: Combinations and Permutations
|
||
|
|
---
|
||
|
|
## Combinations and Permutations
|
||
|
|
|
||
|
|
Let's say you have 9 people competing to place in the top three of a golf tournament. How many different possibilities are there for the top three in the tournament?
|
||
|
|
Well, if we pick first place first, we have 9 people to choose from. After that, we would have 8 to choose from for second place, and 7 for third place. To calculate the total, we simply have to multiply them together:
|
||
|
|
|
||
|
|
9x8x7=505
|
||
|
|
|
||
|
|
This is an example of a permutation. A permutation is the number of different ordered possibilities that can occur in a given situation. A permutation can be with or without repetition, as can a combination. If we say that there is a permutation for n things with r possibilities, the formulae will be:
|
||
|
|
|
||
|
|
#####**With Repetition:**
|
||
|
|
n^r
|
||
|
|
|
||
|
|
#####**Without Repetition:**
|
||
|
|
n\!/(n-r)\!
|
||
|
|
|
||
|
|
Returning to the problem at the top, what if they were sitting in three identical chairs instead of having rankings? This is an example of a combination. In a combination, order doesn't matter. Therefore, every permutation of the same combination has to be eliminated. This creates two more formulae:
|
||
|
|
|
||
|
|
#####**With Repetition:**
|
||
|
|
(r+n-1)\!/(r\!(n-1)\!)
|
||
|
|
|
||
|
|
#####**Without Repetition:**
|
||
|
|
n\!/(r\!(n-r)\!)
|
||
|
|
|
||
|
|
|
||
|
|
###Sources
|
||
|
|
“Combinations and Permutations.” Math is Fun, www.mathsisfun.com/combinatorics/combinations-permutations.html.
|
||
|
|
|
||
|
|
|
||
|
|
<a href='https://github.com/freecodecamp/guides/tree/master/src/pages/mathematics/combinations-and-permutations/index.md' target='_blank' rel='nofollow'>Help our community expand this article</a>.
|
||
|
|
|
||
|
|
<a href='https://github.com/freecodecamp/guides/blob/master/README.md' target='_blank' rel='nofollow'>This quick style guide will help ensure your pull request gets accepted</a>.
|
||
|
|
|
||
|
|
<!-- The article goes here, in GitHub-flavored Markdown. Feel free to add YouTube videos, images, and CodePen/JSBin embeds -->
|
||
|
|
|
||
|
|
#### More Information:
|
||
|
|
<!-- Please add any articles you think might be helpful to read before writing the article -->
|
||
|
|
|
||
|
|
|