In maths, a combination is a selection of items from a collection, such that the order of option does not issue (unlike permutations). For instance, provided three fruits, state an apple, an orange as well as a pear, there are three mixes of 2 that can be drawn from this collection: an apple and a pear; an apple and also an orange; or a pear and also an orange. A lot more formally, a k-combination of an established S is a part of k unique components of S. If the collection has n elements, the number of k-combinations amounts to the binomial coefficient ( n. k. ). =. n. (. n. −. 1. ). ⋯. (. n. −. k. +. 1. ). k. (. k. −. 1. ). ⋯. 1. ,. \ displaystyle = \ frac n( n-1) \ dotsb (n-k +1) , which can be composed using factorials as. n. ! k. ! (. n. −. k. ). ! whenever. k. ≤. n. \ displaystyle k \ leq n , and which is zero when. k. n. \ displaystyle k > n . The collection of all k-combinations of a set S is often represented by. (. S. k. ). \ displaystyle \ textstyle...