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10.3 Combinations

10.3 Combinations. Objectives: Solve problems involving combinations. Solve problems by distinguishing between permutations and combinations. Standards: 2.7.8 A Determine the number of combinations and permutations for an event. p urple/green purple/red p urple/blue p urple/grey.

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10.3 Combinations

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  1. 10.3 Combinations Objectives: Solve problems involving combinations. Solve problems by distinguishing between permutations and combinations. Standards: 2.7.8 A Determine the number of combinations and permutations for an event.

  2. purple/green purple/red purple/blue purple/grey green/purple green/red green/blue green/grey red/purple red/green red/blue red/grey blue/purple blue/green blue/red blue/grey grey/purple grey/green grey/red grey/blue There are 10 possible 2-color combinations.

  3. Recall that a permutationis an arrangement of objects in a specific order. An arrangement of objects in which order is not important is called a combination.

  4. Find the number of ways to purchase 3 different kinds of juice from a selection of 10 different juices.

  5. Find the number of ways to rent 5 comedies from a collection of 30 comedies at a video store. Find the number of combination of 9 objects taken 7 at a time. 6 7 9 13

  6. How many ways are there to give 3 honorable mentions awards to a group of 8 entrants in a contest? How many ways are there to award 1st, 2nd, 3rd prize to a group of 8 entrants in a contest? 8C3= 56 8P3= 336

  7. How many ways are there to choose a committee of 2 people from a group of 7 people? How many ways are there to choose a chairperson and a co-chairperson from a group of 7 people? 7C2= 21 7P2= 42

  8. Consider CD’s, cassettes, and videotapes separately, and apply the fundamental counting principle.

  9. How many different ways are there to purchase 3 CDs, 4 cassettes, and 2 videotapes if there are 3 CD titles, 6 cassette titles, and 4 videotape titles from which to choose? 3C3 x 6C4 x 4C2= 90 Terry is buying paperback books to read while on vacation. How many different ways are there for Terry to purchase 3 novels and 2 non-fiction books if there are 10 novels and 6 nonfiction books to choose from? 10C3 x 6C2= 1800

  10. Using Combinations and Probability In a recent survey of 25 voters, 17 favor a new city regulation and 8 oppose it. Find the probability that in a random sample of 6 respondents from this survey, exactly 2 favor the proposed regulation and 4 oppose it. First, find the number of outcomes in the event. Use the Fundamental Counting Principle. Choose 2 of the 17 in favor. Choose 4 of the 8 who oppose. Next, find the numbers of outcomes in the sample space. Choose 6 from the 25 respondents. Finally, find the probability. Thus, the probability of selecting exactly 2 people in favor and 4 people opposed in a randomly selected group of 6 is about 5%

  11. Thus, the probability of selecting exactly 2 people in favor and 4 people opposed in a randomly selected group of 6 is about 5%

  12. In a recent survey of 30 students, 25 students favored an earlier opening time for the school cafeteria and 5 opposed it. Find the probability that in a random sample of 8 respondents from this survey, exactly 6 favored the earlier opening time and exactly 2 opposed it. First, find the number of outcomes in the event. Use the Fundamental Counting Principle. Choose 6 of the 25 in favor. Choose 2 of the 5 who oppose. Next, find the numbers of outcomes in the sample space. Finally, find the probability. Choose 8 from the 30 respondents. Thus, the probability of selecting exactly 6 students in favor and 2 students opposed in a randomly selected group of 8 is about 30%

  13. HOMEWORKPractice 10.3Quiz TOMORROW on 10.1 – 10.3

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