METHOD
Formula and method
C(n,k)=n!/[k!(n−k)!]; P(n,k)=n!/(n−k)!; Pr(X=k)=C(n,k)p^k(1−p)^(n−k).
Combinations, permutations and binomial probability calculator
Calculate combinations, permutations and binomial probability.
01
Your inputs
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Your result
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About this result
Informational calculations. Check assumptions, dates and jurisdiction before making a decision.
Full disclaimerCombinations versus permutations
Combinations count the ways to choose k items from n when order does not matter, and permutations count them when it does. For n = 10 and k = 3 there are 720 permutations, because 10 · 9 · 8 = 720, and 120 combinations, because each choice of three items appears 3 · 2 · 1 = 6 times among the permutations. Given a success probability p, the calculator also returns the binomial probability of exactly k successes in n independent trials, which is 11.71875% for p = 0.5.
TRACEABLE
Sources and validity
Basic arithmetic or geometry using the formula shown. Uses only your inputs.
How we maintain data