Permutations and Combinations Problem Set
Explore various permutations and combinations scenarios involving arranging items in a particular order or selecting items where order does not matter. Topics covered include choosing lunch items, possible license plate combinations, arranging shirts in a closet, selecting students for presentations, forming sports teams, and more.
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11-1: Permutations & Combinations Warm-Up: How many ways could you choose a sandwich, side dish, and dessert for lunch?
The Fundamental Counting Principle describes the method of using multiplication to count. Use a tree diagram. Each choice branches off of the previous choice. Veggieburger PB & J Cheeseburger Hamburger Potatoes Corn Beans AC B F RP
1) In 1966, one type of Maryland license plate had two letters followed by four digits. How many of this type of license plate were possible? 2) A locker takes three numbers from zero to 25 to open. How many types of number passwords to open a locker are possible? How many are possible if a digit cannot be reused?
Factorial: A permutation is an arrangement of items in a particular order. : choosing r items out of n items total 3) In how many ways can you arrange 8 shirts on hangers in a closet? 4) In how many ways can you arrange 8 shirts on 5 hangers in a closet? 5) In how many ways can 15 runners finish first, second, and third place?
A combination is a selection in which order does not matter. : choosing r items out of n items total 6) Mrs. Vida is selecting 4 students out of 20 to present answers to the class. 7) The coach is selecting 9 players out of 15 to form a baseball team. How can we change each of the above to be a permutation?
FCP, Permutation, or Combination? 1. Fifteen students ask to visit a college admissions counselor. Each scheduled visit includes one student. In how many ways can ten time slots be assigned? 2. The prom committee has four sites available for the banquet and three sites for the dance. How many arrangements are possible for the banquet and dance? 3. There are eight swimmers in a competition where the top three swimmers advance. In how many ways can three swimmers advance? 4. In how many ways can five tires be arranged on a car?
