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10.6 Combinations Fri Nov 22

10.6 Combinations Fri Nov 22. Do Now At a restaurant, a family wants to order 3 appetizers, 3 entrees, and 1 dessert to share. There are 9 appetizers, 15 entrees, and 4 desserts on the menu. How many different dinners can the family order?. HW Review: p.889. Combinations.

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10.6 Combinations Fri Nov 22

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  1. 10.6 CombinationsFri Nov 22 Do Now At a restaurant, a family wants to order 3 appetizers, 3 entrees, and 1 dessert to share. There are 9 appetizers, 15 entrees, and 4 desserts on the menu. How many different dinners can the family order?

  2. HW Review: p.889

  3. Combinations • A combination is an arrangement where the order of the objects do NOT matter • Permutation: A race where 1st 2nd and 3rd place get gold, silver, and bronze medals • Combination: A race where the first 3 finishers get the same medal

  4. Combinations • Because a combination does not consider order, there will be less arrangements compared to a permutation

  5. Combination Notation • The total number of combinations of N objects taken K at a time, is Or

  6. Binomial Coefficient Notation • Another kind of notation for combinations is binomial coefficient notation • This notation will be used in the next section

  7. Ex • Evaluate

  8. Ex • Evaluate and

  9. Equivalent Combinations • Given n total objects, the number of arrangements of k objects out of n, and n-k objects out of n are equal

  10. Ex • Classic Lotto 47 is a twice-weekly lottery game with jackpots starting at $1 million. For a wager of $1, a player can choose 6 numbers from 1-47. If the numbers match those drawn by the state, the player wins • How many 6-number combinations are there?

  11. Ex • How many committees can be formed from a group of 5 governors and 7 senators if each committee consists of 3 governors and 4 senators?

  12. Closure • If the first 3 finishers in a race of 10 people move onto the next round of a tournament, how many different groups of people can move on? • HW: p.897 #1-31 odds

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