Combination
C(n, r) = n! / (r!(n-r)!)
Use when order does not matter and repetition is not allowed.
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Counting formulas reference
A short stable reference for the main counting formulas used across the calculators, answers, quizzes, and problems on this site.
Combination with repetition
C(n + r - 1, r)
Use when order does not matter and repetition is allowed.
Permutation
P(n, r) = n! / (n-r)!
Use when order matters and repetition is not allowed.
Permutation with repetition
n^r
Use when order matters and each ordered position can reuse any option.
Factorial
n!
Multiply every whole number from 1 through n.
Circular permutation
(n - 1)!
Use when rotations count as the same arrangement.
Multiset permutation
n! / (a! b! c! ...)
Use when arranging repeated items such as letters in a word.
Binomial coefficient
C(n, r) = nCr
The notation-focused version of plain combinations.