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)

Learn more about syntax conventions.

Parameters

Name	Type	Required	Description
n	int	✔️	The total number of items.
k	int	✔️	The selected number of items.

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.

Important

A let statement can't run on its own. It must be followed by a tabular expression statement. To run a working example of perm_fl(), see Example.

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.

Important

You must run this code to create the function before you can use the function as shown in the Example.

.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.

Run the query

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

Important

For this example to run successfully, you must first run the Function definition code to store the function.

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

Output

n	k	pnk
3	1	3
6	4	360
9	7	181440