Permutation Calculator
Frequently Asked Questions
What is the difference between permutation and combination?
Permutation counts ordered arrangements — the order of selection matters. Combination counts unordered selections — the order does not matter. Use permutation for rankings, sequences, and positions. Use combination for groups, teams, or committees where no specific ordering is required among the chosen items.
What does nPr mean in the permutation formula?
nPr denotes the number of permutations of n items taken r at a time. It is calculated as n! divided by (n − r)!. Here, n is the total pool of items and r is how many you select and arrange. The exclamation mark represents the factorial — the product of all positive integers up to that number.
Can r be greater than n in a permutation?
No. In standard permutations without repetition, r must be less than or equal to n. If r were greater than n, you would need to reuse items, which changes the formula to n^r (permutation with repetition). This calculator uses the standard no-repetition formula, so always ensure r does not exceed n.
How do I calculate permutations with repetition allowed?
When repetition is allowed, the formula changes to n^r instead of n! / (n − r)!. For example, a 4-digit PIN from 10 digits with repetition allowed gives 10^4 = 10,000 possibilities. This calculator handles the no-repetition case; for repetition, simply raise n to the power of r manually.
What is 0 permutation (r = 0) equal to?
When r equals 0, nPr always equals 1, regardless of n. This is because there is exactly one way to arrange zero items — the empty arrangement. Mathematically, this follows from the factorial rule that 0! equals 1, making n! / n! = 1 for any value of n.
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