Exact result
720
10 permute 3 without repeats is 720.
10P3 counts ordered arrangements of 3 chosen items from 10 distinct items. After the first choice, only 9 unused items remain, then 8, so the count is 10 x 9 x 8. If repetition were allowed, the count would be 10^3 instead, not 10P3.
Worked steps
Show your work
- Inputs: n = 10, r = 3
- Formula: P(n, r) = n! / (n-r)!
- Substitute: P(10, 3) = 10! / (10-3)!
- Steps: 3,628,800 / 5,040
- Result: 10 permute 3 without repeats is 720.
Interactive tool
Verify the same values in the calculator
10P3 counts ordered arrangements of 3 chosen items from 10 distinct items. After the first choice, only 9 unused items remain, then 8, so the count is 10 x 9 x 8. If repetition were allowed, the count would be 10^3 instead, not 10P3.
Result
0
Enter values to calculate.
What your result means
The explanation updates with the current inputs.
Live visual
Fruit preview
Previewing a small sample keeps the page fast and readable.
Calculation work