🔗 Combination Calculator
Calculate nCr combinations from n items
How Combination Calculation Works
Formula
C(n, r) = n! / (r! × (n − r)!)
- 1Enter the total number of items (n).
- 2Enter how many items to choose (r).
- 3The calculator computes n!, r!, and (n−r)! factorials.
- 4It divides n! by the product of r! and (n−r)!.
- 5The result is the number of unique groups, regardless of order.
About Combination Calculator
Calculate combinations (nCr) — how many ways to choose r items from n without regard to order. Shows formula, step-by-step solution, and Pascal's triangle relationships.
Frequently Asked Questions
What is the difference between combinations and permutations?
Combinations don't care about order — choosing {A,B,C} is the same as {C,B,A}. Permutations consider order, so those would be two different arrangements. Use combinations for groups, permutations for sequences.
What does 'n choose r' mean?
It means: from a set of n items, how many unique groups of r items can you form? For example, '5 choose 2' = 10, meaning there are 10 unique pairs from 5 items.
What is C(n,0) and C(n,n)?
Both equal 1. C(n,0) = 1 because there's exactly one way to choose nothing. C(n,n) = 1 because there's exactly one way to choose all items.