Combinatorics Calculator
Calculate the number of ways to arrange or select items from a set. Essential for probability theory, statistics, and algorithm design.
Permutation ($nPr$)
0
Combination ($nCr$)
0
Order matters for $nPr$, but not for $nCr$.
Arrangements vs. Selections
The fundamental difference between these two concepts is Order. If the sequence of items changes the outcome, use Permutations. If you only care about which items are picked, use Combinations.
- Permutation Formula: $P(n,r) = \frac{n!}{(n-r)!}$
- Combination Formula: $C(n,r) = \frac{n!}{r!(n-r)!}$
Frequently Asked Questions
When should I use nPr? +
Use Permutations when order is important. Examples include picking a President, VP, and Secretary from a group, or creating a unique password from a set of characters.
When should I use nCr? +
Use Combinations when the order doesn't matter. Examples include picking 3 students to join a committee, or being dealt a hand of cards in a game.
What does the "!" mean? +
It stands for "Factorial." For example, $5! = 5 \times 4 \times 3 \times 2 \times 1 = 120$. By definition, $0!$ is equal to 1.
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