Combination C(n,r) or ^nCr = n!/(r!(n-r)!) counts selections of r objects from n distinct objects where order does NOT matter. Formula: ^nCr = ^nP(n,r)/r!. Example: C(5,3) = 5!/(3! × 2!) = 10. Properties: C(n,r) = C(n, n-r); C(n,0) = 1; C(n,n) = 1. Applications: Committee selection, lottery draws, group formations. Comparison: P(5,3) = 60 (ordered), C(5,3) = 10 (unordered). Solving: Identify if order matters. If yes, use permutation; if no, use combination. Shortcut: C(n,r) = C(n,r-1) × (n-r+1) / r (sequential calculation). Exam tip: Committee selection, choosing teams always use combination. Seating, ranking always use permutation.