SQL Server PERMUTATIONA Function

Updated 2024-03-13 13:09:18.090000

Description

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

P_{k,n}=n^k

Syntax

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

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.

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);