Dax Function: COMBINA

Category: Statistical Functions

The COMBINA function in Power BI calculates the number of combinations (with repetitions allowed) for selecting a specified number of items from a set. It is useful when the same item can be chosen multiple times.

Purpose

To compute combinations where repetition of items is allowed.

Type of Calculations

Combinatorial mathematics, considering duplicate selections.

Practical Use Cases

  • Scenarios involving grouping with replacement, such as creating combinations of flavors, materials, or resources.
  • Probability and statistics problems where elements can appear more than once.
  • Inventory or SKU analysis in business when repeat items are possible.

COMBINA(number, number_chosen)
ParameterTypeDescription
numberScalarThe total number of items. Must be a non-negative integer.
number_chosenScalarThe number of items to choose, including repetitions. Must be a non-negative integer.

How Does COMBINA Dax Works

The formula used by the COMBINA function is:

Where:

  • nn is the total number of items (number).

  • rr is the number of items chosen at a time (number_chosen).

  • (n+r−1)! denotes the factorial of (n+r−1), which is the product of all positive integers up to (n+r−1).

Example Calculation

For COMBINA(5, 3):

What Does It Return?

The function returns an integer value:

  • Represents the total number of combinations possible when selecting number_chosen items from number items, allowing repetitions.

  • The result is always a non-negative integer.

When Should We Use It?

  • When calculating combinations where duplicate selection of items is allowed.

  • Useful in inventory modeling, customer choice analysis, or menu planning.

  • To determine the total number of outcomes in repeated-selection probability problems.

Examples

Basic Usage :

Calculate the number of ways to choose 3 items (with replacement) from a set of 4:


COMBINA(4, 3)

Output: 20

Column Usage

Apply the function dynamically to data in columns:


COMBINA(Table[TotalItems], Table[ChosenItems])

This computes combinations for each row based on the values in TotalItems and ChosenItems.

Advanced Usage

Combine COMBINA with conditional functions:


IF(COMBINA(10, 4) > 50, "High Combinations", "Low Combinations")

This evaluates the combinations and categorizes them based on a threshold.

Tips and Tricks

  • Include Repetitions: Use COMBINA specifically when repetitions are allowed; for combinations without repetitions, use COMBIN.

  • Input Validation: Ensure input parameters are non-negative integers to avoid errors.

  • Factorial Limits: Large values for number or number_chosen may lead to factorial overflow; pre-compute or approximate for large datasets.

Potential Pitfalls

  • Parameter Constraints: Ensure number and number_chosen are logical for the context. Negative or non-integer values will result in errors.

  • Performance on Large Data: Factorial-based calculations can be resource-intensive for large numbers.

Performance Impact of COMBINA DAX Function:

  • Efficient for small to medium datasets.

  • For large datasets, pre-compute combinations to optimize performance and avoid factorial overflow.

Related Functions You Might Need

  • COMBIN: Calculates combinations without repetition.

  • PERMUT: Calculates permutations where the order of selection matters.

  • FACT: Computes the factorial of a number.

Want to Learn More?
For more information, check out the official Microsoft documentation for COMBINA You can also experiment with this function in your Power BI reports to explore its capabilities.

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1. What does the COMBINA function do?

It calculates the number of combinations with repetitions allowed.

2. How is COMBINA different from COMBIN?

COMBINA allows repeated selections, whereas COMBIN does not.

3. What happens if number_chosen is 0?

The function returns 1, as there is only one way to select nothing.

4. Can COMBINA handle fractional inputs?

No, both number and number_chosen must be non-negative integers.

5. What are practical applications of the COMBINA function?

It is used in inventory management, customer choice modeling, and scenarios where repetition is allowed.

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