Combination nCr = n!/[r!(n-r)!] counts selections where order does not matter. The relationship nPr = r! * nCr shows that each combination generates r! permutations. Key properties: nCr = nC(n-r) (choosing r to include = choosing n-r to exclude), Pascal's identity nCr + nC(r-1) = (n+1)Cr, and the row sum C(n,0) + C(n,1) + ... + C(n,n) = 2^n = total subsets. For computational ease, use the smaller of r and n-r. Committee formation is the classic combination problem. When constraints exist (at least k from a subgroup), either enumerate cases or use complementary counting. Selection with repetition allowed: C(n+r-1, r) where n = number of types, r = number to select.