Combination Calculator (nCr): Selections Where Order Does Not Matter
Enter n and r to count the ways of choosing r items from n when order does not matter. Answers are exact, even with hundreds of digits.
- Nothing you type is stored
- Free
- No signup
Result
25,98,960
- Number of digits
- 7
- Same as
- 52C5 = 52C47
Combinations ignore order: {A, B} is the same as {B, A}.
Show working
- ⁿCᵣ = n! / (r!(n − r)!)
- = 52! / (5!·47!)
- = (52 × 51 × 50 × 49 × 48) / (5 × 4 × 3 × 2 × 1)
- = 2598960
How to use
- Enter n, the total number of items.
- Enter r, how many you choose.
- Choose whether repetition is allowed and read nCr.
Good to know
Formula: nCr = n!/(r!(n − r)!). Example: 5-card hands from a 52-card deck: 52C5 = 25,98,960. Choosing a 3-person committee from 10 people: 10C3 = 120.
Symmetry: nCr = nC(n − r), because choosing r items to keep is the same as choosing n − r to leave out. The calculator uses the smaller one for speed.
With repetition (choosing r scoops from n flavours, repeats allowed) the count is (n + r − 1)Cr. Big results are exact integers, shown in scientific form when very long.
Questions
What is 10C3?
10 × 9 × 8 / (3 × 2 × 1) = 120.
When do I use combination instead of permutation?
When only the group matters, not the order: teams, committees, lottery numbers, card hands.
What is nC0 or nCn?
Both equal 1: one way to choose nothing, and one way to choose everything.
How is nCr linked to Pascal’s triangle?
Row n of Pascal’s triangle lists nC0, nC1, …, nCn, and each entry is the sum of the two above it.
Is my data stored or sent anywhere?
No. The calculation runs entirely in your browser; nothing you type leaves your device.