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Chapter 9

Number functions 145

Combination

Format

Combination(setSize;numberOfChoices)

Parameters

setSize - any numeric expression or field containing a non-negative numeric

expression.

numberOfChoices - any numeric expression or field containing a non-negative numeric

expression.

Data type returned

number

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.

Example

Combination(5;2) returns 10 for a set consisting of {a, b, c, d, e} because the unique

choices when choosing two at a time are {ab, ac, ad, ae, bc, bd, be, cd, ce, de}.

(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).

Div

Format

Div(number;divisor)

Parameters

number - any numeric expression or field containing a numeric expression

divisor - any numeric expression or field containing a numeric expression

Data type returned

number

Combination

Factorial setSize, numberOfChoices()

Factorial numberOfChoices()

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Filemaker TH325Z/A Fiche technique Page 145