10.3 Combinations Objectives: Solve problems involving combinations. Solve problems by distinguishing between permutations and combinations. Standards:

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Presentation transcript:

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

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.

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)! {n MATH to PRB # 3 r}

Ex 2. Find the number of ways to rent 5 comedies from a collection of 30 comedies at a video store. Ex 3. Find the number of combination of 9 objects taken 7 at a time. 30 C 5 = 142,506 9 C 7 = 36

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? 8 C 3 = 56 8 P 3 = 336

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? 7 C 2 = 21 7 P 2 = 42

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? 3 C 3 * 6 C 4 * 4 C 2 = C 3 * 6 C 2 = 1800

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 ( 25 C 6 * 5 C 2 ) =.30 = 30% 30 C 8

Writing Activities

Review of Combinations

Homework Integrated Algebra II- Section 10.3 Level A Academic Algebra II- Section 10.3 Level B