comb_fl()

Calculate C(n, k)

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

Syntax

comb_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 comb_fl=(n:int, k:int)
{
    let fact_n = gamma(n+1);
    let fact_nk = gamma(n-k+1);
    let fact_k = gamma(k+1);
    tolong(fact_n/fact_nk/fact_k)
};
// 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 combinations for selection of k items out of n items without order")
comb_fl(n:int, k:int)
{
    let fact_n = gamma(n+1);
    let fact_nk = gamma(n-k+1);
    let fact_k = gamma(k+1);
    tolong(fact_n/fact_nk/fact_k)
}

Example

Query-defined

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

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

Stored

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

Output