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Calculate combinations (C(n,r)) with support for different types: with/without repetition, binomial coefficients, and detailed combinatorial analysis.
Execution
Fill in the form, run the tool, and review the result in one place.
Samples
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Tool usage guide
The Combination Calculator is a precise mathematical tool designed to compute the number of ways to select items from a larger set, supporting both standard combinations and combinations with repetition.
Background
A manager needs to select a 3-person committee from a team of 10 employees.
Problem
Calculate how many unique committee combinations are possible.
How to use
Set n=10, r=3, and select 'Without Repetition'.
n=10, r=3, type=without_repetitionOutcome
The tool returns 120 possible unique committee combinations.
Background
A student is buying a 3-scoop bowl of ice cream from 10 available flavors, where flavors can be repeated.
Problem
Find the total number of flavor combinations possible with repetition allowed.
How to use
Set n=10, r=3, and select 'With Repetition'.
n=10, r=3, type=with_repetitionOutcome
The tool calculates 220 possible combinations for the ice cream bowl.
Without repetition means each item can be selected only once. With repetition allows the same item to be chosen multiple times.
No, combinations specifically ignore the order of selection. If order matters, you should use a permutation calculator instead.
The calculator supports values for n and r up to 50.
Yes, by enabling the 'Show mathematical formula' option, the tool will display the specific formula applied to your inputs.
This feature identifies the specific row and column index where your combination result appears within Pascal's triangle.