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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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