Quick guide
How to use this calculator
- Enter the total number of distinct objects n.
- Enter the number of ordered positions r.
- Read the exact number of ordered selections.
Calculation method
Fill each ordered position
There are n choices for the first position, n−1 for the second, and so on for r positions.
Worked example
Award three places among ten people
First, second, and third place are different roles, so order matters.
P(10,3) = 10!/7! = 720
Supported inputs
Precision and limits
Discrete domain
Inputs are whole counts. Negative, fractional, grouped, and scientific-notation inputs are rejected.
Exact integers
Results use arbitrary-precision integers and are never rounded. Inputs and output size are bounded to keep the page responsive.