SQL Server LPERMUT Function

Updated 2024-03-08 21:45:15.067000

Description

Use the scalar function LPERMUT to calculate the natural logarithm of the PERMUT function. The PERMUT function calculates the number of permutations without replacement defined as:

_nP_k=\frac{n!}{\left(n-k\right)!

Syntax

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

Arguments

@n

Number of items.

@k

Number chosen.

Return Type

float

Remarks

If n < 0 then NULL is returned.

If k < 0 then NULL is returned.

If k > n then NULL is returned.

Examples

Example #1

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

This produces the following result.

LPERMUT
6.5792512120101

Example #2

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

SELECT x.n,
       1 - EXP(wct.LPERMUT(365, x.n) - wct.LPERMUTA(365, x.n)) as [p(n)]
FROM
(
    VALUES
        (10),
        (20),
        (22),
        (23),
        (30),
        (57)
) x (n);