How many ways can you arrange or pick a subset? The answer depends on whether order matters (permutation) or doesn't (combination).
Permutations of n taken r at a time
P(n, r) = n! / (n − r)!
Combinations of n taken r at a time
C(n, r) = n! / (r! (n − r)!)
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How many ways to arrange 3 letters from A, B, C, D?
Order matters → permutations. P(4, 3) = 4 × 3 × 2 = 24.
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How many ways to pick 3 students from 10?
Order doesn't matter → combinations. C(10, 3) = 120.