Permutation & Combination Calculator
Calculate permutations and combinations with and without repetition for counting problems.
Permutations
720
P(10, 3) = 10! / (10-3)!
Combinations
120
C(10, 3) = 10! / (3! × (10-3)!)
n!
3,628,800
r!
6
Key Difference
Permutations
Order matters - different arrangements count separately
Combinations
Order doesn't matter - only selection matters
What are Permutations and Combinations?
Permutations count arrangements where order matters. Combinations count selections where order doesn't matter. Both are fundamental counting principles.
Formulas
Permutations: P(n,r) = n!/(n-r)!. Combinations: C(n,r) = n!/(r!(n-r)!). The combination formula divides by r! to account for duplicate orderings.
Applications
Permutations: passwords, race positions, seating arrangements. Combinations: lottery numbers, selecting a committee, choosing ingredients.