# 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

Name Type Required Description
n int, long, or real ✔️ The total number of items.
k int, long, or real ✔️ 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:

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 `comb_fl()`, see Example.

``````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.
``````

## Example

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)
``````

Output

n k cnk
3 1 3
6 4 15
9 7 36