nCr

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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