# 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*`)`

Learn more about syntax conventions.

## 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 |

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