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Combination()Category: Number Syntax: Combination ( setSize ; numberOfChoices ) Parameters: setSize ”any expression that returns a non-negative numeric value; numberOfChoices ”any expression that returns a non-negative numeric value. Description: Returns the number of ways to uniquely choose numberOfChoices items from a set of size setSize . The values returned by this function are referred to as combination coefficients . They form Pascal's triangle. This function is useful in statistics, combinatorics, and polynomial expansions. The formula used to determine the Combination value is n! / (n-x)! * x! , where n = set size, x = number of choices. Examples : Combination ( 4 ; 2 ) Returns 6 , because there are 6 ways of selecting 2 items from a set of 4 items. Given set { A, B, C, D} , these subsets would be { AB, AC, AD, BC, BD, CD}. Combination ( x ; 0 ) Returns 1 for any x, representing the empty set. Combination ( x ; x ) Returns 1 for any x. (13 * 12 * Combination(4;2) * Combination(4;3)) / Combination(52;5) Returns 0.00144057... , which is the probability of being dealt a full house in 5-card poker (less than a 1% chance). Comments : The numbers returned by the Combination function are the coefficients of the binomial expansion series. For instance, (x + y) 4 = 1x 4 + 4x 3 y + 6x 2 y 2 + 4xy 3 + 1y 4 Combination ( 4 ; 0 ) = 1 Combination ( 4 ; 1 ) = 4 Combination ( 4 ; 2 ) = 6 Combination ( 4 ; 3 ) = 4 Combination ( 4 ; 4 ) = 1 |
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