Daily DAX : Day 213 COMBINA

 The COMBINA function in Power BI DAX calculates the number of combinations with repetitions allowed for a given number of items. It’s useful in scenarios where you need to determine how many ways you can select a certain number of items from a set, where the order doesn’t matter and items can be chosen more than once.

Syntax

COMBINA(number, number_chosen)

    number: The total number of items (must be a non-negative integer).

    number_chosen: The number of items to choose in each combination (must be a non-negative integer).

Return Value

Returns an integer representing the number of possible combinations with repetitions.

Formula

The COMBINA function uses the mathematical formula for combinations with repetition:

COMBINA(n, k) = C(n + k - 1, k) = (n + k - 1)! / (k! * (n - 1)!)

Where:

    n = number

    k = number_chosen

    ! denotes factorial (e.g., 5! = 5 × 4 × 3 × 2 × 1).

Key Points

    If either argument is negative, COMBINA returns an error.

    If non-integer inputs are provided, they are truncated to integers.

    Unlike the COMBIN function, COMBINA allows repetitions (e.g., selecting the same item multiple times).

Use Case

Scenario: A business analyst is modeling a product bundling strategy. A store offers 5 types of pastries, and customers can choose 3 pastries for a bundle, where they can pick the same pastry multiple times (e.g., 3 croissants or 2 croissants + 1 donut). The analyst needs to calculate how many unique bundle combinations are possible.

DAX Example:

dax

Total_Bundles = COMBINA(5, 3)

Result: 

    For 5 pastries and 3 choices, COMBINA(5, 3) = 35.

    This means there are 35 possible ways to create a bundle (e.g., {Croissant, Croissant, Croissant}, {Croissant, Croissant, Donut}, {Croissant, Donut, Muffin}, etc.).

Calculation Breakdown:

    Using the formula: COMBINA(5, 3) = C(5 + 3 - 1, 3) = C(7, 3) = 7! / (3! * 4!) = (7 × 6 × 5) / (3 × 2 × 1) = 35.

Practical Application in Power BI

    Create a Measure: Use COMBINA in a measure to calculate combinations dynamically based on user inputs or slicers.

    dax

    Possible_Combinations = COMBINA(SELECTEDVALUE(Table[Total_Items]), SELECTEDVALUE(Table[Items_Chosen]))

    Visualize: Display the result in a card or table to show the number of combinations for business decisions, like inventory planning or marketing strategies.

    Scenario Analysis: Use COMBINA to evaluate scenarios like product bundles, team formations, or resource allocations where repetitions are allowed.

Example in Context

Dataset: A table with columns Total_Items (e.g., 5 pastries) and Items_Chosen (e.g., 3).

Measure:

dax

Combinations = COMBINA(Table[Total_Items], Table[Items_Chosen])

Output: For Total_Items = 5 and Items_Chosen = 3, the measure returns 35, which can be visualized in a report to inform bundle pricing or promotion strategies.

Limitations

    COMBINA can produce large numbers for high inputs, so ensure your use case handles large results.

    It’s purely mathematical and doesn’t account for real-world constraints (e.g., stock availability).

In summary, COMBINA is a powerful DAX function for calculating combinations with repetitions, ideal for business scenarios like product bundling, resource allocation, or probabilistic modeling in Power BI reports.