Combinations 0.4. Combinations: a selection of r objects from a group on n objects where the order is not important.

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Presentation transcript:

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. 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

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? 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, , ,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 b) 2 cheeses and 4 toppings c) 3 cheeses and 1 topping d) 2 cheeses or 3 toppings

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