12.8 The Counting Principle and Permutation

• The Counting Principle states that if an experiment can be performed in M ways and a second experiment can be performed in N ways, then the two experiments, in that order, can be performed in M×N ways.
• A permutation is any ordered arrangement of a set of objects.
• n! - (n factorial)
  • n! = n × (n-1) × (n-2) × ... × 2 × 1
• If you have n items, they can be arranged in n! permutations.
• _nP_r = n!/(n-r)!
• If you have n items, and you want to arrange r of them there are _nP_r permutations.
• If you have n items to arrange, but n₁, n₂, ... n_k duplicates occur, then there are n!/(n₁! × n₂! × ... ×n_k!) permutations.
• Do page 799, 11, 22, 23, 31, 33, 36, 56

12.9 Combinations

• A combination is a set of objects without regard to their arrangement.
• _nC_r = n!/ ((n-r)!× r!)
• Dp page 806 numbers 25, 29, 38