Permutation P(n,r)
Combination C(n,r)
Permutation w/ Rep. n^r
Combination w/ Rep.
Factorial n!
FAQ
What is the difference between permutation and combination?
Permutation considers order, combination does not. For example, selecting 2 from A, B, C: permutations are AB, BA, AC, CA, BC, CB (6 total); combinations are AB, AC, BC (3 total). Formula: P(n,r)=n!/(n-r)!, C(n,r)=n!/(r!(n-r)!)
What is permutation with repetition?
Permutation with repetition allows the same element to be selected multiple times. The formula is n^r. For example, a 4-digit PIN has 10⁴=10,000 possible combinations. This is useful for password and key space calculations.
What is a factorial n!?
Factorial n! = n×(n-1)×(n-2)×...×2×1. For example, 5!=120. By convention, 0!=1. Factorials grow extremely fast: 20!≈2.4×10¹⁸. This tool uses BigInt for large number calculations.
Where are permutations and combinations used?
Common use cases: 1) Probability theory event counting; 2) Cryptography key space calculation; 3) Lottery probability; 4) Scheduling and roster planning; 5) Tournament arrangements; 6) Sampling survey design.