Answers Permutation Calculator

What is 10P3?

This is a permutation without repetition because the P notation means an ordered selection from distinct items, and standard nPr notation assumes you do not reuse an item after choosing it.

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

  1. Inputs: n = 10, r = 3
  2. Formula: P(n, r) = n! / (n-r)!
  3. Substitute: P(10, 3) = 10! / (10-3)!
  4. Steps: 3,628,800 / 5,040
  5. Result: 10 permute 3 without repeats is 720.

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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.

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