1. 15.3 Counting Methods: Combinations ©2002 by R. Villar All Rights Reserved

2. Combinations In the last lesson, you learned that order is important for some counting problems. For other counting problems, order is not important. For example, in most card games, the order in which your cards are dealt is not important. After your cards are dealt, reordering them does not change your card hand. These unordered groupings are called combinations. A combination is a selection of r objects from a group of n objects where the order is not important. Combinations of n Objects Taken r at a Time: The number of combinations of r objects taken from a group of n distinct objects is: Notice that this formula is the same one given for binomial coefficients in Chapter 12.

3. How many different combinations of rides can you go on if you want to ride at least 15 of them? This means that you can ride on 15, 16, 17, 18, 19, or 20 rides... Example: An amusement park has 20 different rides. You want to ride exactly 15 of them. How many different combinations of rides can you go on? = 15504 different ways Total combinations = = 21700 different ways = 15504 + 4845 +1140 + 190 + 20 + 1

4. B. What is the probability that the cards are 10, Jack, Queen, King, and Ace of the same suit? P = successes possible outcomes Example: A standard deck of 52 playing cards has 4 suits with 13 different cards in each suit. A. If the order in which the cards are dealt is not important, how many different 5 card hands are possible? = 2,598,960 different hands = 4 2,598,960 = 1 649,740 Since there are 4 different suits (hearts, diamonds, clubs, spades)