Daily DAX : Day 268 FACT

 The `FACT` function in Power BI's DAX (Data Analysis Expressions) calculates the factorial of a given number. The factorial of a non-negative integer \( n \) is the product of all positive integers less than or equal to \( n \) (e.g., \( 5! = 5 \times 4 \times 3 \times 2 \times 1 = 120 \)).

### Syntax

```

FACT(<number>)

```

- **`<number>`**: A non-negative integer (or a value that can be truncated to an integer) for which to calculate the factorial.

- Returns: The factorial of the input number as a double-precision floating-point number.

### Key Points

- The input must be a non-negative integer or a value that can be converted to one (e.g., 5.7 is truncated to 5).

- If the input is negative, `FACT` returns an error.

- The maximum input value is typically 170, as factorials beyond this exceed the double-precision limit in DAX.

- If the input is not an integer, it is truncated (e.g., `FACT(5.9)` calculates `FACT(5)`).

### Use Case

The `FACT` function is primarily used in scenarios involving combinatorial calculations, such as:

- **Calculating permutations or combinations**: For example, determining the number of ways to arrange or select items.

- **Statistical or probability models**: Used in formulas for binomial coefficients, such as \( \binom{n}{k} = \frac{n!}{k!(n-k)!} \).

- **Financial or operational modeling**: Useful in scenarios requiring factorial-based calculations, like scheduling or resource allocation.

### Example

Suppose you have a Power BI table with a column `Items[Count]` containing the number of items to arrange. You want to calculate the number of possible arrangements (permutations).

#### DAX Formula

```dax

TotalArrangements = FACT(Items[Count])

```

#### Scenario

- If `Items[Count] = 5`, the measure calculates `FACT(5) = 120`, meaning there are 120 ways to arrange 5 items.

- In a Power BI report, you could use this measure to display the number of possible arrangements for each item count in a table or visual.

#### Combination Example

To calculate combinations (e.g., \( \binom{n}{k} \)), you can combine `FACT` with other DAX functions:

```dax

Combinations = 

DIVIDE(

    FACT(Items[Count]),

    FACT(Items[Selected]) * FACT(Items[Count] - Items[Selected])

)

```

- Here, `Items[Count]` is \( n \), and `Items[Selected]` is \( k \). This calculates the number of ways to choose \( k \) items from \( n \).

### Practical Notes

- **Performance**: Factorials grow extremely large quickly, so use `FACT` cautiously with large numbers to avoid overflow or performance issues.

- **Validation**: Ensure inputs are non-negative integers to avoid errors.

- **Alternatives**: For complex combinatorial logic, consider using DAX functions like `COMBIN` or `PERMUT` if they directly meet your needs.

This function is niche but powerful for specific mathematical or statistical use cases in Power BI.