Combinations & Permutations Calculator
Count every possible outcome.
Combinations & Permutations Calculator
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What This Calculator Does
The Combinations & Permutations Calculator computes both C(n,r) and P(n,r) in one step. Combinations count groups where order does not matter. Permutations count arrangements where order does matter.
How It Works
C(n,r) = n! / (r! x (n-r)!). P(n,r) = n! / (n-r)!.
Example
From 10 items choose 3: C(10,3) = 120, P(10,3) = 720.
Formula
C = n!/(r!(n-r)!), P = n!/(n-r)!Reading the Results
Combinations C(n,r)
The number of ways to choose r items from n where order does not matter.
Permutations P(n,r)
The number of ways to arrange r items from n where order matters.
Frequently Asked Questions
When do I use combinations vs permutations?
Use combinations when order does not matter (picking a team). Use permutations when order matters (ranking).
What does C(n,r) mean?
It counts the number of distinct groups of size r that can be formed from n items.
What is the relationship between combinations and permutations?
C(n,r) = P(n,r) / r!. The permutations formula counts order; dividing by r! removes the ordering.