Permutations & Combinations Calculator
Solve nPr & nCr Arrangements and SubsetsStep-by-Step Mathematical Expansion
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Solutions
Combinations: C(10, 3)
nCr = 120
Unordered subsets (Order does NOT matter)
Permutations: P(10, 3)
nPr = 720
Ordered arrangements (Order matters)
Permutations w/ Repetition (nʳ):1,000
Combinations w/ Repetition:220
Frequently Asked Questions
• Permutation (Order Matters): Picking 1st, 2nd, and 3rd place in a race, or a PIN code (1-2-3 is different from 3-2-1).
• Combination (Order Does NOT Matter): Picking a hand of 5 cards in poker, or picking 3 team members from a committee (Alice, Bob, Carol is the same as Carol, Bob, Alice).
• Combination (Order Does NOT Matter): Picking a hand of 5 cards in poker, or picking 3 team members from a committee (Alice, Bob, Carol is the same as Carol, Bob, Alice).
• nPr (Permutations) =
• nCr (Combinations) =
n! / (n − r)!• nCr (Combinations) =
n! / [r! × (n − r)!]