Statistics

Permutation Calculator (nPr)

Count ordered arrangements of r items chosen from n.

Calculated Output

Permutations 720

Formula: nPr = n! ÷ (n − r)!

Step-by-Step Breakdown

1. Values used:

2. Total items (n) = 10

3. Chosen (r) = 3

5. Permutations = 720

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The math behind it

nPr = n! ÷ (n − r)! = n × (n − 1) × … × (n − r + 1).

Top-3 finish from 10 runners → 10P3 = 10 × 9 × 8 = 720 orders.

When do I use permutations?

When order matters — like rankings, passwords or seating arrangements.