Editing Binomial coefficient (section)

== Combinatorics and statistics ==
Binomial coefficients are of importance in [[combinatorics]] because they provide ready formulas for certain frequent counting problems:
* There are <math>\tbinom n k</math> ways to choose ''k'' elements from a set of ''n'' elements. See [[Combination]].
* There are <math>\tbinom {n+k-1}k</math> ways to choose ''k'' elements from a set of ''n'' elements if repetitions are allowed. See [[Multiset]].
* There are <math> \tbinom {n+k} k</math> [[string (computer science)|strings]] containing ''k'' ones and ''n'' zeros.
* There are <math> \tbinom {n+1} k</math> strings consisting of ''k'' ones and ''n'' zeros such that no two ones are adjacent.<ref>{{cite journal|last=Muir|first=Thomas|title=Note on Selected Combinations|journal=Proceedings of the Royal Society of Edinburgh|year=1902|url=https://books.google.com/books?id=EN8vAAAAIAAJ&pg=GBS.PA102}}</ref>
* The [[Catalan number]]s are <math>\tfrac{1}{n+1}\tbinom{2n}{n}.</math>
* The [[binomial distribution]] in [[statistics]] is <math>\tbinom n k p^k (1-p)^{n-k} .</math>