What is the difference between COMBINA and COMBIN?

COMBIN calculates combinations without repetition (each item can be selected only once), while COMBINA allows repetition in selections. For example, COMBIN(5,2) gives 10 combinations, but COMBINA(5,2) gives 15 combinations because repeated selections are permitted.

Can COMBINA handle zero as a parameter value?

Yes, COMBINA can handle zero values. COMBINA(n,0) always returns 1 (one way to choose nothing), and COMBINA(0,0) also returns 1. However, COMBINA(0,k) where k is greater than zero returns 1 as well, following combinatorial principles.

What is the maximum value COMBINA can calculate?

COMBINA can handle very large numbers, but results are limited by Excel's numerical precision. The function can work with numbers up to 2^53-1 (approximately 9 quadrillion), though practical results are typically much smaller due to the nature of combinatorial calculations.

How does COMBINA relate to probability calculations?

COMBINA is fundamental in probability theory for calculating sample spaces. By determining the total number of possible combinations with repetition, you can divide favorable outcomes by COMBINA results to calculate probabilities in scenarios where items can be selected multiple times.

Can I use COMBINA with arrays or ranges?

COMBINA requires scalar values (single numbers) for both parameters, not arrays or ranges. If you need to calculate combinations for multiple scenarios, you must either create separate formulas or use array formulas with helper columns to apply COMBINA across different value pairs.

Master the COMBINA Function: Calculate Combinations with Repetition in Excel

Intermediate

=COMBINA(number, number_chosen)

The COMBINA function is a powerful mathematical tool in Excel that calculates the number of combinations with repetition allowed. Unlike the standard COMBIN function, COMBINA enables you to determine how many ways you can choose items from a group when repetition is permitted. This distinction is crucial for real-world scenarios where selections can be repeated, such as choosing multiple products from a catalog, assigning team members to projects with possible duplicates, or calculating password combinations. Understanding COMBINA is essential for data analysts, statisticians, and business professionals who work with probability calculations and combinatorial analysis. Whether you're developing inventory models, analyzing survey responses, or building predictive models, mastering this function will enhance your analytical capabilities. The COMBINA function has been available since Excel 2013, making it a reliable tool across modern Excel versions including 2016, 2019, and Microsoft 365.

Syntax & Parameters

The COMBINA function uses a straightforward syntax: =COMBINA(number, number_chosen). The first parameter, 'number,' represents the total count of items available in your pool from which selections will be made. This value must be a positive integer greater than or equal to zero. The second parameter, 'number_chosen,' specifies how many items you want to select from that pool, also requiring a non-negative integer. The mathematical principle behind COMBINA involves the formula: (n+k-1)! / (k! × (n-1)!), where n is the total number of items and k is the number of items chosen. This differs fundamentally from COMBIN, which calculates combinations without repetition using the formula n! / (k! × (n-k)!). When using COMBINA, both parameters must be numeric values; if either contains text or is omitted, Excel will return a #VALUE! error. The function returns an integer representing the total number of possible combinations, making it ideal for probability analysis and combinatorial problems where items can be selected multiple times.

number

Total number of items

number_chosen

Number of items to choose

Practical Examples

Ice Cream Flavor Selection

=COMBINA(8,3)

With 8 flavors and the ability to choose 3 scoops with repetition allowed, the function calculates all possible combinations including scenarios like vanilla-vanilla-chocolate or strawberry-strawberry-strawberry.

Project Team Assignment

=COMBINA(5,4)

This calculates how many ways to distribute 4 task assignments among 5 available team members, accounting for the possibility that one person might handle multiple tasks.

Survey Response Combinations

=COMBINA(6,3)

This formula helps understand the total sample space of possible responses when survey participants can indicate the same preference multiple times across three selection slots.

Key Takeaways

COMBINA calculates combinations with repetition allowed, using the formula (n+k-1)!/(k!(n-1)!), making it essential for scenarios where items can be selected multiple times
Unlike COMBIN, COMBINA produces larger result values because it accounts for duplicate selections, fundamentally changing probability and statistical calculations
Both parameters must be non-negative numeric integers; text values or negative numbers will produce #VALUE! or #NUM! errors
COMBINA is available in Excel 2013 and later versions (2016, 2019, 365) and serves as a critical tool for combinatorial analysis, probability calculations, and business scenario modeling

Pro Tips

Use named ranges for COMBINA parameters to create more readable and maintainable formulas. For example, define 'TotalItems' and 'ItemsToChoose' ranges, then use =COMBINA(TotalItems,ItemsToChoose) for clarity.

Impact : Improves formula readability, reduces errors when updating values, and makes your spreadsheet more professional and easier to audit.

Create a lookup table with COMBINA results for common scenarios. Pre-calculate combinations for standard ranges (e.g., 1-20 items, 1-10 selections) to avoid repeated calculations and improve spreadsheet performance.

Impact : Dramatically speeds up workbook recalculation time, especially in complex models with thousands of combination calculations, and provides instant reference for stakeholders.

Always validate your parameters before using COMBINA in critical calculations. Use data validation rules to restrict entries to positive integers and prevent formula errors from propagating through dependent calculations.

Impact : Prevents cascading errors, ensures data integrity, and saves debugging time by catching invalid inputs before they affect your analysis.

Document the mathematical context of your COMBINA formulas with comments explaining why repetition is allowed and what real-world scenario the calculation represents.

Impact : Ensures that other users (or your future self) understand the combinatorial logic, making the spreadsheet more maintainable and reducing misinterpretation of results.

Useful Combinations

COMBINA with SUM for Multiple Scenarios

=SUM(COMBINA(A2:A10,B2))

Combine COMBINA with SUM to calculate total combinations across multiple groups. This array formula sums the combinations for each row, useful when analyzing combinations across different product categories or team structures simultaneously.

COMBINA with IF for Conditional Calculations

=IF(B1>A1,"Invalid",COMBINA(A1,B1))

Use IF to validate that number_chosen doesn't exceed number before calculating. This prevents unexpected results and adds data validation logic to your combinatorial analysis.

COMBINA with ROUND for Probability Percentages

=ROUND(1/COMBINA(10,3)*100,2)

Combine COMBINA with ROUND and division to calculate the probability percentage of a specific combination occurring. This is useful for probability analysis and statistical reporting in business contexts.

Common Errors

#VALUE!

Cause: One or both parameters contain non-numeric values, such as text strings, empty cells, or logical values. For example: =COMBINA("eight",3) or =COMBINA(8,"three")

Solution: Ensure both parameters are numeric values. Convert text to numbers using VALUE() function if necessary, or verify that cell references point to cells containing actual numbers, not formatted text.

#NUM!

Cause: Parameters are negative numbers or exceed Excel's numerical limits. COMBINA requires non-negative integers. Example: =COMBINA(-5,3) or =COMBINA(5,-2)

Solution: Verify that both number and number_chosen are positive integers or zero. Use ABS() function to convert negative values to positive if appropriate for your calculation.

#REF!

Cause: The formula references cells that have been deleted or moved, breaking the cell reference chain. Example: =COMBINA(A1,B1) where column A or B has been deleted.

Solution: Check that all referenced cells still exist in the workbook. Re-enter the formula with correct cell references, or use the Find & Replace feature to update broken references.

Troubleshooting Checklist

1.Verify both parameters are numeric values and not text strings, even if they look like numbers
2.Confirm that both number and number_chosen are non-negative integers (greater than or equal to zero)
3.Check that cell references haven't been deleted or moved, causing #REF! errors in your formula
4.Ensure you're using COMBINA (with repetition) rather than COMBIN (without repetition) for your specific scenario
5.Test the formula with known values to verify the calculation is producing expected results before applying to large datasets
6.Validate that your interpretation of 'combinations with repetition' matches your actual business requirement

Edge Cases

COMBINA(0,0) - Choosing zero items from zero items

Behavior: Returns 1, following mathematical convention that there is exactly one way to choose nothing from nothing

This edge case is mathematically correct and useful in recursive algorithms or when validating combinatorial logic

COMBINA(1,1000) - Choosing many items from only one available item

Behavior: Returns 1, because with only one item available and repetition allowed, there is only one possible combination (all selections are the same item)

This demonstrates that COMBINA correctly handles scenarios where the pool is smaller than the number of selections needed

Very large numbers: COMBINA(1000,500)

Behavior: May return extremely large numbers that approach Excel's numerical limits, potentially resulting in precision loss or display issues

Solution: Use scientific notation or convert results to text for display; consider using logarithmic transformations for probability calculations instead of raw combination counts

Excel can handle the calculation but displaying such large numbers may require special formatting or alternative representations

Limitations

•COMBINA only accepts scalar values; it cannot directly process arrays or ranges without helper columns or array formulas, limiting its flexibility in complex multi-dimensional analyses
•Results are limited by Excel's numerical precision (approximately 15-16 significant digits); extremely large combination calculations may lose precision or exceed display capabilities
•COMBINA cannot be used in conditional formatting rules or data validation formulas directly, requiring workarounds with helper columns for dynamic validation based on combination calculations
•The function provides no built-in way to generate the actual combinations themselves—it only counts them—requiring additional logic or external tools to list specific combinations

Alternatives

COMBIN Function

Calculates combinations without repetition, providing different results when items cannot be reused

When: Use when selecting unique items from a pool, such as choosing 3 unique team members from 10 available staff for a specific project

PERMUT Function

Calculates permutations (order matters) instead of combinations (order doesn't matter), accounting for sequence

When: Use when the arrangement order is important, such as determining possible rankings or seating arrangements

FACT Function

Calculates factorial values, which are building blocks for manual combination and permutation calculations

When: Use when creating custom combinatorial formulas or when you need to manually calculate combinations using the formula n!/(k!(n-k)!)

Compatibility

✓ Excel

Since Excel 2013

=COMBINA(number, number_chosen) - Fully supported in Excel 2013, 2016, 2019, and Microsoft 365 with identical syntax and behavior

✓Google Sheets

=COMBINA(number, number_chosen) - Google Sheets supports COMBINA with identical syntax and functionality as Excel

Results are consistent with Excel; no version limitations as Google Sheets automatically updates

✓LibreOffice

=COMBINA(number, number_chosen) - LibreOffice Calc supports COMBINA with the same syntax and mathematical principles as Excel

Frequently Asked Questions

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