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

3. I.Combination of n Objects Taken r at a Time – the number of combinations of n objects taken r at a time, is given by C (n, r) = n C r = ( nr) = __ _n! ___, where 0 < r < n. r! (n – r)! I.Combination of n Objects Taken r at a Time – the number of combinations of n objects taken r at a time, is given by C (n, r) = n C r = ( nr) = __ _n! ___, where 0 < r < n. r! (n – r)!

4. Ex 2. How many different sets of 5 comedies can you rent from a collection of 30 comedies at a video store. Ex 3. Find the number of combinations of 9 objects taken 7 at a time.

6. c). How many ways are there to give 3 honorable mentions awards to a group of 8 entrants in a contest? d). How many ways are there to award 1st, 2nd, 3rd prize to a group of 8 entrants in a contest?

7. Ex 5. 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?

9. Ex 7. 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? Ex 8. 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?

10. II. Using Combinations and Probability Ex 1. 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. Ex 2. 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. (17 C 2 * 8 C 4) =.05 = 5% 25 C 6

11. Writing Activities

12. Review of Combinations