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Permutations & Combinations

Learn how to calculate the number of possible meals, answer keys, phone numbers, license plates, magazine readings, and more. Understand permutations and combinations with examples and formulas. Use graphing calculator functions for quick calculations. Get a homework worksheet for practice.

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Permutations & Combinations

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  1. Permutations & Combinations

  2. Counting Principle • If there are 3 meats, 5 vegetables, and 2 types of bread to choose from for a meal, how many different meals are possible?

  3. How many answer keys are possible for a 5 question true/false quiz?

  4. How many 7-digit phone numbers are possible?

  5. If a license plate has 3 letters followed by 3 numbers, how many plates are possible?

  6. How many ways can I read six magazines out of 10?

  7. Permutation – order is important • Suppose that a club with 12 members wishes to choose a president, a vice-president, and a treasurer. • The order is important. • How many ways can this be done?

  8. Can you develop a formula for finding a permutation? Let’s check to see if you’re right:

  9. Combination – order doesn’t matter • Suppose the club merely wants to choose a governing council of 3. • Now for each governing council of 3 that can be chosen (say A, B, C) there are ____ different slates of officers. In other words they are the same.

  10. So how many governing councils are there?

  11. Can you develop a formula for Combinations? Let’s check to see if you’re right!

  12. I want to take three books out of my collection of 10 to school to put on my desk. How many ways can this be done?

  13. A company advertises two job openings for computer programmers, both with the same salary and job description. In how many ways can the openings be filled if 8 people apply?

  14. A company advertises two job openings, one for a copywriter and one for an artist. If 10 people who are qualified for either position apply, in how many ways can the openings be filled?

  15. For a certain raffle, 845 tickets are sold. In how many ways can four $50 gift certificates be awarded?

  16. How many ways can a $100, a $50, a $20, and a $10 gift certificate be awarded?

  17. Permutations & Combinations can be done on the graphing calculator! • Type the n (# of items) • Press math, Prb • Choose the appropriate key (#2 or #3) • Type the r (# chosen) • Press enter

  18. How many ways can I choose six people for a committee in a class of 20?

  19. How many ways can I select four bikes from seven?

  20. At the Red Lion Diner, an omelet can be ordered plain or with any or all of the following fillings: cheese, onions, peppers. How many different kinds of omelets are possible?

  21. There are 8 different kinds of cookies and 11 different cakes. How many ways can I choose 3 types of cookies and 5 different cakes?

  22. There are 10 different magazines and 12 different books. How many ways can I choose 3 if I want at most 2 books?

  23. How many permutations are in the word letter?

  24. How many permutations are in the word Mississippi?

  25. Homework • Worksheet

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