Combinations (nCr) Calculator
Use this free combinations (nCr) calculator to find the number of combinations. Enter total items (n) and the number of items to choose (r), and get your result instantly.
What Are Combinations?
Combinations represent the number of ways to select items from a group where the order does not matter. For example, choosing 2 fruits from {apple, banana, orange} gives {apple, banana}, {apple, orange}, and {banana, orange}. In combinations, {apple, banana} is the same as {banana, apple}.
Formula for Combinations (nCr)
The formula to calculate combinations is:
nCr = n! / [r! × (n − r)!]
- n = total number of items
- r = number of items chosen
- ! = factorial, the product of all positive integers up to that number
Example Calculation
Example: How many ways can you choose 3 students from 8?
n = 8, r = 3
8C3 = 8! / (3! × 5!) = (8 × 7 × 6) / (3 × 2 × 1) = 56
There are 56 possible combinations.
Combination vs Permutation
| Feature | Combination | Permutation |
|---|---|---|
| Order Matters | No | Yes |
| Formula | nCr = n! / [r!(n−r)!] | nPr = n! / (n−r)! |
| Example | Choosing 2 fruits | Arranging 2 fruits |