nCr

Stub grade: A

This page is a stub

This page is a stub, so it contains little or minimal information and is on a to-do list for being expanded.The message provided is:

I'd like this page to be better, "" for Combinations and what is noted there. Alec (talk) 16:38, 14 April 2018 (UTC)

Definition

$n$-choose-$r$ is the number of ways to choose $r$ items from $n$ items, said differently it's the number of distinct combinations of length $r$ we can make from $n$ items.

• $$\text{nCr}(n,r):\eq\frac{n!}{r!(n-r)!}$$

Notation

I write and prefer something like: ${}^nC_r$ - but I've never gotten this to work well in LaTeX.

I've also seen $\left(\begin{array}{c}n\\r\end{array}\right)$ used, but more compact (vertically) than this vector.

Properties

• $n\text{C}r(n,r)\eq n\text{C}r(n,n-r)$

See also

• nPr - the same concept but for number of permutations instead.
• Pascal's triangle