Permutations P(10, 3)
720
Order matters
Combinations C(10, 3)
120
Order doesn't matter
Formulas
P(n, r) = n! / (n − r)!
C(n, r) = n! / (r! · (n − r)!)
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PickOrder
Permutations count ordered arrangements; combinations count unordered selections. Both formulas, both answers, every time.
Permutations P(10, 3)
720
Order matters
Combinations C(10, 3)
120
Order doesn't matter
Formulas
P(n, r) = n! / (n − r)!
C(n, r) = n! / (r! · (n − r)!)
Use P(n,r) when arrangement matters — picking a 1st, 2nd, 3rd place. Use C(n,r) when it doesn't — picking a 5-person team from 10 people.