Calculate nPr (permutations) and nCr (combinations) with step-by-step solutions
Allow Repetition
Items can be reused
Choose n and r to see permutations or combinations
P(n,r) = n! / (n-r)!
Order matters: arrangement of items
P(5,3) = 5!/(2!) = 120/2 = 60
C(n,r) = n! / (r! × (n-r)!)
Order doesn't matter: selection of items
C(5,3) = 5!/(3!×2!) = 120/(6×2) = 10
Permutations and combinations are fundamental concepts in probability and statistics. They help us count the number of ways to arrange or select items from a set.
Order matters! Different arrangements of the same items count as different permutations.
Example: P(3,2) from {A,B,C}
AB, AC, BA, BC, CA, CB (6 permutations)
Order doesn't matter! Different arrangements of the same items count as the same combination.
Example: C(3,2) from {A,B,C}
AB, AC, BC (3 combinations)
Calculating odds in games, lotteries, and gambling
Chance of winning lottery: C(49,6)
Number of possible password combinations
8-character password: 94^8 permutations
Poker hand probabilities, card distributions
Poker hands: C(52,5)
Gene combinations in offspring
Genetic trait combinations
Sampling methods, survey design
Selecting samples from population
Match scheduling, ranking possibilities
Number of possible rankings
| n | n! | Value |
|---|---|---|
| 0 | 0! | 1 |
| 1 | 1! | 1 |
| 2 | 2! | 2 |
| 3 | 3! | 6 |
| 4 | 4! | 24 |
| 5 | 5! | 120 |
| 6 | 6! | 720 |
| 7 | 7! | 5,040 |
| 8 | 8! | 40,320 |
| 9 | 9! | 362,880 |
| 10 | 10! | 3,628,800 |