Counting and Permutations

• The Counting Principle states that if one experiment can be performed m distinct ways (or has m outcomes) and a second experiment can be performed n distinct ways (or has n outcomes), then the two experiments, in that order can be performed m×n ways.
• Selecting two cards from a deck.
• Rolling a die twice.
• Simple Counting problems
• Some notation
  • n! = n·(n-1)·(n-1)...3·2·1
    • for integer n, n > 0.
    • If n = 0, n!= 1 by definition
• A permutation is an ordered arrangement of a set of objects.
  • We will use permutation when order matters.
  • A permutation of n objects can be performed in n! ways.
  • If we are only selecting a subset of the objects, the number of items is noted as _nP_r = n!/(n-r)!
• Do some problems 742