In mathematics, a combination is a selection of items from a collection, such that the order of selection does not matter (unlike permutations). For example, given three fruits, say an apple, an orange and a pear, there are three combinations of two that can be drawn from this set: an apple and a pear; an apple and an orange; or a pear and an orange.More formally, a k-combination of a set S is a subset of k distinct elements of S. If the set has n elements, the number of k-combinations is equal to the binomial coefficient
( n k ) = n ( n − 1 ) ⋯ ( n − k + 1 ) k ( k − 1 ) ⋯ 1 , {\displaystyle {\binom {n}{k}}={\frac {n(n-1)\dotsb (n-k+1)}{k(k-1)\dotsb 1}},}which can be written using factorials as n ! k ! ( n − k ) ! {\displaystyle \textstyle {\frac {n!}{k!(n-k)!}}} whenever k ≤ n {\displaystyle k\leq n} , and which is zero when k > n {\displaystyle k>n} . The set of all k-combinations of a set S is often denoted by ( S k reference
Ever curious about what that abbreviation stands for? fullforms has got them all listed out for you to explore. Simply,Choose a subject/topic and get started on a self-paced learning journey in a world of fullforms.
Allow To Receive Free Coins Credit 🪙