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12-6 Permutations and Combinations

Learn how to use the multiplication counting principle, permutations, and combinations to solve various counting problems. Includes examples and practice problems.

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12-6 Permutations and Combinations

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  1. 12-6 Permutations and Combinations

  2. Multiplication Counting Principle If there are m ways to make a first selection and n ways to make a second selection, then there are ways to make two selections EXAMPLE: For 5 shirts and 8 pairs of shorts, the number of possible outfits is

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

  4. Problem 2: Finding 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?

  5. Problem 2: Using Permutation Notation The expression represents the number of permutations of n objects arranged r at a time EXAMPLE:

  6. A band has 7 new songs and wants to put 5 of them on a demo CD. How many arrangements of 5 songs are possible?

  7. Problem 3: 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:

  8. Twenty people report for jury duty. How many 12-different person juries can be chosen?

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