perm_fl()

Calculate P(n, k)

The function perm_fl() is a user-defined function (UDF) that calculates P(n, k), the number of permutations for selection of k items out of n, with order. It’s based on the native gamma() function to calculate factorial, (see facorial_fl()). For selection of k items without order, use comb_fl().

Syntax

perm_fl(n, k)

Parameters

Function definition

You can define the function by either embedding its code as a query-defined function, or creating it as a stored function in your database, as follows:

Query-defined

Define the function using the following let statement. No permissions are required.

let perm_fl=(n:int, k:int)
{
    let fact_n = gamma(n+1);
    let fact_nk = gamma(n-k+1);
    tolong(fact_n/fact_nk)
};
// Write your query to use the function here.

Stored

Define the stored function once using the following .create function. Database User permissions are required.

.create-or-alter function with (folder = "Packages\\Stats", docstring = "Calculate number of permutations for selection of k items out of n items with order")
perm_fl(n:int, k:int)
{
    let fact_n = gamma(n+1);
    let fact_nk = gamma(n-k+1);
    tolong(fact_n/fact_nk)
}

Example

Query-defined

To use a query-defined function, invoke it after the embedded function definition.

let perm_fl=(n:int, k:int)
{
    let fact_n = gamma(n+1);
    let fact_nk = gamma(n-k+1);
    tolong(fact_n/fact_nk)
}
;
range n from 3 to 10 step 3
| extend k = n-2
| extend pnk = perm_fl(n, k)

Stored

range n from 3 to 10 step 3
| extend k = n-2
| extend pnk = perm_fl(n, k)

Output