COMBINATION TEMPERATURE SERVICE
see Combination (disambiguation) . "COMBIN" redirects here. For other uses · see Combin (disambiguation) . Selection of items from a set In mathematics · a combination is a selection of items from a set that has distinct members · 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 . So · the number of k -combinations · denoted by C ( n · k ) {\displaystyle C(n · k)} or C k n {\displaystyle C_{k}^{n}} · is equal to the binomial coefficient : ( n k ) = n ( n − · 1 ) ⋯ · ( n − · k + 1 ) k ( k − · {\displaystyle {\binom {n}{k}}={\frac {n(n-1)\dotsb (n-k+1)}{k(k-1)\dotsb 1}}
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2212; 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 using factorial notation can be compactly expressed as ( n k ) = n ! k ! ( n − k ) ! {\displaystyle {\binom {n}{k}}={\frac {n!}{k!(n-k)!}}} whenever n ≥ k ≥ 0 {\displaystyle n\geq k\geq 0} . This formula can be derived from the fact that each k -combination of a set S of n members has k ! {\displaystyle k!} permutations
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