1. Combinations 0.4

2. Combinations: a selection of r objects from a group on n objects where the order is not important.

3. Example 1: a) Find the # of ways to purchase 3 different kinds of juice from a selection of 10 different juices. b) Find the # of ways to rent 4 comedy DVDs from a collection of 9 comedy DVDs. c) Find the # of ways 3 students can be selected from a committee of 5. 120 126 10

4. Deck of Cards How many cards are in a standard deck? How many suits and what are they? How many cards in each suit? How many face cards? How many of each number or face?

6. Multiply or Add ??? *When you are finding the # of ways both event A and event B can occur… MULTIPLY *When you are finding the # of ways that event A or event B can occur…. ADD

7. Example 2 Deck of cards: when dealt a hand, the order you receive the cards does not matter. a) Using a standard deck of 52 cards, how many different 7-card hands are possible? b) How many of these 7 card hands have 2 jacks, 3 sevens, and 2 aces? c) How many of these 7 card hands have 4 kings and 3 other cards? d) How many of these hands have all 7 cards of the same suit? e) How many possible 5 card hands contain exactly 3 kings? 133,784,560 6864 17,296 144 4,512

8. Example 3 A pizza parlor offers a selection of 3 different cheeses and 9 different toppings. In how many ways can a pizza be made with the following: a) 1 cheese and 2 toppings b) 2 cheeses and 4 toppings c) 3 cheeses and 1 topping d) 2 cheeses or 3 toppings 108 378 9 87

9. Permutation or Combination?? *Permutations: ORDER MATTERS *Combinations: ORDER DOES NOT MATTER Example 3: Decide if the situation is a permutation or combination. a) 4 recipes were selected for publication and 302 recipes were submitted. b) 4 out of 200 contestants were awarded prizes of $100, $75, $50, and $25. c) A president and vice-president are elected for a class of 210 students. d) Nine players are selected for a team of 15 to start the baseball game. e) The batting order for the 9 starting players is announced. Perm Comb