How to calculate combinations with the combination calculator
Start with two counts. Enter Number of items (n), enter Number chosen (r), then select No repetition or Allow repetition. Select Calculate to see the nCr count, the formula, the calculation steps, and text you can copy or download.
- Enter a whole number in Number of items (n).
- Enter a whole number in Number chosen (r).
- Choose No repetition or Allow repetition.
- Select Calculate to show Result and Formula & steps.
- Select Copy result or Download result (.txt) to keep the displayed text.
- Select Reset to clear both fields, restore No repetition, and hide the current result.
What an nCr calculator counts
A combination counts a selection once when order does not change the selection. Choosing items A and B gives the same result as choosing B and A. The result is a count of possible selections, with no unit attached.
For five items with two chosen and No repetition, the result is ten:
Number of items (n): 5
Number chosen (r): 2
No repetition
Combinations = 10How combinations with repetition change the formula
No repetition uses C(n, r) = n! / (r! × (n - r)!). Each item can be selected once, so r cannot exceed n. Allow repetition uses C(n + r - 1, r), so the same item can be selected again.
With three item types and two selections, Allow repetition gives six outcomes:
Number of items (n): 3
Number chosen (r): 2
Allow repetition
C(3 + 2 - 1, 2) = 6Result includes Given, Formula, a symmetry or edge-case note when one applies, and the final result. Formula & steps does not show each internal loop calculation.
Combination calculator input limits and edge cases
Both fields accept whole numbers from 0 through 10,000. Leave a field empty, enter a non-numeric value, or enter a number above 10,000, and the calculator shows an error. With No repetition, it also rejects r > n.
When r = 0, both modes return 1. With Allow repetition, n = 0 and r > 0 returns 0. No repetition rejects those values because the requested selection is larger than the available set.
When to use a permutation calculator instead
Use this combination calculator when order does not change the choice, such as selecting committee members. Choose the Permutation Calculator when different orders count as different arrangements. The Factorial Calculator handles factorial and derangement values. The Number Theory Calculator covers several number-theory operations. The Math Calculators category also includes tools for equations, geometry, sequences, matrices, vectors, and scientific calculations.
Where combination counts come up
A teacher can count groups of students when seating order is irrelevant. A card-game exercise can count hands drawn from a deck, with No repetition because a physical card is selected once.
A product planner can count sets of options when an item may be selected again, using Allow repetition. Enter the total item types as n and the selection size as r.
Frequently asked questions
What does a combination calculator calculate?
It counts unordered ways to choose r items from n items. Select No repetition or Allow repetition to choose the calculation mode, then select Calculate to show the formula and steps.
What is the nCr formula without repetition?
Without repetition, nCr is C(n, r) = n! / (r! × (n - r)!). The calculation uses symmetry by working with the smaller of r and n - r.
How do I calculate combinations with repetition?
Select Allow repetition, then enter n and r. The calculator uses C(n + r - 1, r), so an item can appear more than once in a selection.
Why does the combination calculator reject my values?
Each field must contain a whole number from 0 through 10,000. With No repetition, r must be less than or equal to n.
What is the difference between combinations and permutations?
Combinations treat different orders as the same selection. Permutations count those orders separately, so use the Permutation Calculator when arrangement order is part of the result.