P(10, 3)
= 720
Counts ordered selections of three distinct items from ten.
Large Number Permutations Calculator (nPr)
Compute exact nPr permutations. Count ordered selections from distinct items without replacement.
How this calculation works
P(n, r) counts ordered arrangements of r items selected from n distinct items. It multiplies n × (n − 1) through r factors. Unlike combinations, changing the order produces a different arrangement.
Inputs and accuracy
Enter non-negative whole numbers with the selected count r no larger than the available count n. Repetition is not included in this formula; P(n, 0) is one.
When to use it
Count podium finishes among distinct contestants or ordered assignments to different positions. When order is irrelevant, use the combinations calculator instead.
Worked examples
P(5, 5)
= 120
Arranging all five items is equivalent to 5!.
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