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CombiLab
How many ways can you arrange or choose r items from n?
Permutations count arrangements where order matters (1st, 2nd, 3rd place in a race), while combinations count selections where it doesn't (which 3 people are on a committee) — the same n and r produce a much larger permutation count.
Password/PIN possibilities, lottery odds, team selection, and probability problems in general all reduce to counting permutations or combinations correctly — getting the wrong one is one of the most common probability mistakes.
Permutations (nPr)
720
nPr = n!/(n−r)! · nCr = n!/(r!(n−r)!)
What you entered
n! (factorial of n)
10!= 3628800(n − r)!
(10 − 3)!= 5040Permutations: order matters
10! ÷ (10 − 3)!= 720r! (factorial of r)
3!= 6Combinations: order doesn't matter
10! ÷ (3! × (10 − 3)!)= 120Result
Permutations (nPr): 720
Choosing 3 from 10 items: 720 ways if order matters, 120 ways if it doesn't.