PERMUTATIONA

Updated 2024-03-13 13:09:18.090000

Syntax

SELECT [westclintech].[wct].[PERMUTATIONA] (
   <@n, int,>
  ,<@k, int,>)

Description

Use the scalar function PERMUTATIONA to calculate the number of permutations with replacement defined as:

P_{k,n}=n^k

Arguments

@n

Number of items.

@k

Number chosen.

Return Type

float

Remarks

If n < 0 and k < 0 then NULL is returned.

If k < 0 then NULL is returned.

Examples

Example #1

SELECT wct.PERMUTATIONA(10, 3) as PERMUTATIONA;

This produces the following result.

{"columns":[{"field":"PERMUTATIONA","headerClass":"ag-right-aligned-header","cellClass":"ag-right-aligned-cell"}],"rows":[{"PERMUTATIONA":"1000"}]}

Example #2

Calculate the probability of 2 people having the same birthday in a room containing n people.

SELECT x.n,

       1 - wct.PERMUT(365, x.n) / wct.PERMUTATIONA(365, x.n) as [p(n)]

FROM

(

    VALUES

        (10),

        (20),

        (22),

        (23),

        (30),

        (57)

) x (n);