Permutation and Combination Calculator
Calculate permutations (nPr) and combinations (nCr) instantly. Determine the number of ways to arrange or select items from a set, with or without order.
Standard calculations assume items are distinct and repetition is not allowed.
Difference Between Permutation and Combination
The main difference is whether order matters.
- Permutation (Order matters): Arranging books on a shelf, the code to a safe (1-2-3 is different from 3-2-1), determining Gold/Silver/Bronze winners.
- Combination (Order doesn't matter): Picking players for a team, selecting pizza toppings, choosing lottery numbers (usually).
Example
Suppose you have 3 fruits: Apple, Banana, and Cherry. You want to pick 2.
- Permutations (Order matters): Apple-Banana, Banana-Apple, Apple-Cherry, Cherry-Apple, Banana-Cherry, Cherry-Banana.
Result: 6 ways ($P(3,2) = 6$). - Combinations (Order doesn't matter): {Apple, Banana}, {Apple, Cherry}, {Banana, Cherry}.
Result: 3 ways ($C(3,2) = 3$).
? Frequently Asked Questions
'n' is the total number of items in the set. 'r' is the number of items you are selecting or arranging from that set.
In standard calculations without repetition, no. You cannot pick more items than you have. However, with repetition allowed, r can be greater than n.
The exclamation mark stands for Factorial. It means multiplying a number by every integer below it down to 1. Example: 4! = 4 × 3 × 2 × 1 = 24.