Combinations 0 4 Combinations a selection of r

Combinations 0. 4

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

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

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?

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

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? 133, 784, 560 b) How many of these 7 card hands have 2 jacks, 3 sevens, and 2 aces? 144 c) How many of these 7 card hands have 4 kings and 3 other cards? 17, 296 d) How many of these hands have all 7 cards of the same suit? 6864 e) How many possible 5 card hands contain exactly 3 kings? 4, 512 • •

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 108 b) 2 cheeses and 4 toppings 378 c) 3 cheeses and 1 topping 9 d) 2 cheeses or 3 toppings 87

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. Comb b) 4 out of 200 contestants were awarded prizes of $100, $75, $50, and $25. Perm c) A president and vice-president are elected for a class of 210 students. Perm d) Nine players are selected for a team of 15 to start the baseball game. Comb e) The batting order for the 9 starting players is announced. Perm