Permutations: arranging 3 books from 5 gives P(5,3) = 60 arrangements. Order matters (Book A first is different from Book B first).
Combinations: selecting 3 books from 5 gives C(5,3) = 10 selections. Order is ignored (selecting A,B,C is the same as C,A,B).
The difference: every combination can be arranged in k! ways. So P(n,k) = C(n,k) × k!. Combinations count fewer outcomes because duplicates are merged.