How to use: Calculate permutations and combinations for counting arrangements and selections. Select Type: Permutation nPr (order matters) or Combination nCr (order doesn't matter). Enter Total Items (n) and Items Selected (r). Formulas: Permutation = n!/(n-r)!, Combination = n!/[r!(n-r)!]. Examples: 5 people, choose 3 for ordered podium (1st, 2nd, 3rd) = 5P3 = 60 permutations. 5 people, choose 3 for committee (no order) = 5C3 = 10 combinations. Applications: password possibilities (permutations), lottery odds (combinations), tournament brackets, team selection, seating arrangements, menu choices. Combinations always ≤ permutations for same n,r. Essential for probability, statistics, and counting problems.