42 lines
2.0 KiB
Markdown
42 lines
2.0 KiB
Markdown
---
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title: Combinations and Permutations
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---
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## Combinations and Permutations
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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?
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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:
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9x8x7=505
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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:
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#####**With Repetition:**
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n^r
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#####**Without Repetition:**
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n\!/(n-r)\!
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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:
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#####**With Repetition:**
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(r+n-1)\!/(r\!(n-1)\!)
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#####**Without Repetition:**
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n\!/(r\!(n-r)\!)
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###Sources
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“Combinations and Permutations.” Math is Fun, www.mathsisfun.com/combinatorics/combinations-permutations.html.
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<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>.
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<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>.
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