13-3 Permutations and Combinations. Fundamental Counting Principle.

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13-3 Permutations and Combinations

Fundamental Counting Principle

Problem 1: Using the Fundamental Counting Principle A pizza shop offers 4 crust types, 8 vegetable toppings, and 6 meat toppings. How many different pizzas can you order with one meat topping and one vegetable topping?

Problem 2: Finding the Number of Permutations Permutation: an arrangement of objects in a specific order EXAMPLE: How many different batting orders can you have with 9 players? Example: A swimming pool has 8 lanes. In how many ways can 8 swimmers be assigned lanes for a race?

Problem 3: Using Permutation Notation

Twelve swimmers compete in a race. In how many possible ways can the swimmers finish 1 st, 2 nd, and 3 rd ?

Problem 4: Using Combination Notation Combination: a selection of objects without regard to order. The expression represents the number of combinations of n objects chosen r at a time. Example:

Suppose that you choose 4 books to read on summer vacation from a reading list of 12 books. How many different combinations of the books are possible?

Problem: 5 Identifying Combinations or Permutations