Calculate nCr, nPr, and versions with repetition – instantly
Permutations (Order Matters)
P(10,3) = 720
nPr = n × (n-1) × ... × (n-r+1)
Combinations (Order Doesn't Matter)
C(10,3) = 120
nCr = n! / (r! × (n-r)!)
P(10,3) = 10 × 9 × 8
C(10,3) = 10! / (3! × 7!)
Our advanced Combinations and Permutations Calculator is the ultimate tool for students, teachers, statisticians, data scientists, and anyone working with probability, combinatorics, or counting problems. Instantly calculate nCr (combinations), nPr (permutations), and versions with repetition — with clear formulas and step-by-step explanations.
Whether you're solving lottery odds, arranging passwords, selecting teams, analyzing survey data, or studying discrete mathematics, this calculator delivers accurate results in milliseconds. Understand the difference between order mattering (permutations) and not mattering (combinations) with real-world examples.
No manual factorial calculations — get nCr and nPr in milliseconds.
Calculate arrangements where items can be repeated (e.g., PIN codes).
Perfect for learning discrete math, probability, and statistics concepts.
Lottery odds, password strength, team selection, survey sampling, and more.
n = total number of items, r = number to choose or arrange.
Use for passwords, PINs, or when items can repeat.
See both permutations and combinations with formulas.
Use permutations when order matters (e.g., arranging people in a line, passwords). Use combinations when order doesn't matter (e.g., selecting a committee, lottery numbers).
It means the same item can be chosen more than once. Example: forming a 4-digit PIN where digits can repeat (1111 is allowed).
C(n,r) = P(n,r) ÷ r! → Because permutations count all orders, but combinations treat all orders of the same items as one.
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