10.3 Combinations **Quiz over Tomorrow**

Think back…  Recall from lesson 10.2 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.

Compare:  The number of ways to listen to 2 of 5 CDs is 5 P 2. If you wanted to find the number of ways to purchase 2 of 5 CDs, their order does not matter. This is because they are combined in the total purchase.  To find the amount of combinations of 2CDs taken from 5CDs, divide 5 P 2 by 2 to compensate for the duplicate combinations.

Combinations of n Objects Taken r at a time  The number of combinations of n objects taken r at a time, is given by:

Example 1:  Find the number of ways to purchase 3 different kinds of juice from a selection of 10 different juices.

You Try:  Find the number of combinations of 9 objects taken 7 at a time.

Example 2:  Use permutation or combination to answer each question: How many ways are there to choose a committee of 3 people from a group of 5 people? How many ways are there to choose 3 separate officeholders (chairperson, secretary, and treasurer) from a group of 5 people?

Example 3:  How many different ways are there to purchase 2 CDs, 3 cassettes, and 1 videotape if there are 7 CD titles, 5 cassette titles, and 3 videotape titles from which to choose?

Using Combinations and Probability  Recall from Lesson 10.1 that you can find the probability of event A by using the following ratio:

Using Combinations and Probability  In many situations, you can find and evaluate the numerator and the denominator by applying the formula for combinations.

Example 4:  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. Survey of 25 people 17 favor8 oppose (2 of 17)(4 of 8)

Practice Makes Perfect…  P. 647 #9-39odd