Difference between revisions of "NCr"
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(Created page with "{{DISPLAYTITLE:nCr}}{{Stub page|grade=A|msg=I'd like this page to be better, "" for Combinations and what is noted there. ~~~~}} __TOC__ ==Definition== {{M|n}}-choose-{{M|...") |
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* [[nPr]] - the same concept but for number of [[permutations]] instead. | * [[nPr]] - the same concept but for number of [[permutations]] instead. | ||
* [[Pascal's triangle]] | * [[Pascal's triangle]] | ||
| + | ==Notes== | ||
| + | <references group="Note"/> | ||
| + | ==References== | ||
| + | <references/> | ||
| + | {{Definition|Combinatorics}} | ||
Latest revision as of 16:39, 14 April 2018
Stub grade: A
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I'd like this page to be better, "" for Combinations and what is noted there. Alec (talk) 16:38, 14 April 2018 (UTC)
Definition
[ilmath]n[/ilmath]-choose-[ilmath]r[/ilmath] is the number of ways to choose [ilmath]r[/ilmath] items from [ilmath]n[/ilmath] items, said differently it's the number of distinct combinations of length [ilmath]r[/ilmath] we can make from [ilmath]n[/ilmath] items.
- [math]\text{nCr}(n,r):\eq\frac{n!}{r!(n-r)!} [/math]
Notation
I write and prefer something like: [ilmath]{}^nC_r[/ilmath] - but I've never gotten this to work well in LaTeX.
I've also seen [ilmath]\left(\begin{array}{c}n\\r\end{array}\right)[/ilmath] used, but more compact (vertically) than this vector.
Properties
- [ilmath]n\text{C}r(n,r)\eq n\text{C}r(n,n-r)[/ilmath]
See also
- nPr - the same concept but for number of permutations instead.
- Pascal's triangle
