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Warm Up – Please list: (Please use tree diagrams, and then list the events)

Warm Up – Please list: (Please use tree diagrams, and then list the events). How many ways can we arrange 3 objects A, B, and C: Using just two How many ways can we arrange 4 objects, A, B, C, & D: Using only two Using only three Keep this. We will get back to this later today!. 6. 12.

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Warm Up – Please list: (Please use tree diagrams, and then list the events)

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  1. Warm Up – Please list:(Please use tree diagrams, and then list the events) How many ways can we arrange 3 objects A, B, and C: Using just two How many ways can we arrange 4 objects, A, B, C, & D: Using only two Using only three Keep this. We will get back to this later today! 6 12 24

  2. Math I UNIT QUESTION: How do we determine the number of options if order does not matter? Standard: MM1D1.b Today’s Question: How can we find the number of ways to select 9 people out of 20 for a party? Standard: MM1D1.b.

  3. Combinations • What if order does not matter? Let’s go back to the warm-up: • How many ways can we organize 3 things, using just two of them, if order does matter? • How many redundancies do we have if order does not matter? • How may ways can we organize 3 things if order does not matter? • How can we represent this? 3!/(number of redundancies) 6 2 3

  4. How many ways can we select 2 things from 4 unique things if order does matter? • How many ways can we select 2 things from 4 unique things if order does not matter? Make a tree diagram. • Answer: 6 • Note that we have 2 variations for every choice we pick, which can be written as 2! • How can we represent this?

  5. Combinations • A combination is a selection of r object from a group of n objects without regard to order and is denoted by • The number of combinations of r objects selected from a group of n objects is:

  6. Example 1 • How many different ways are there to select two class representatives from a class of 20 students?

  7. Solution • The answer is given by the number of 2-combinations of a set with 20 elements. • This is often stated as 20 elements, taking 2 at a time • The number of such combinations is

  8. Example 2 From your class of 24, the teacher is randomly selecting 3 to help Mr. Boland with a project. How many combinations are possible?

  9. Your turn! For your school pictures, you can choose 4 backgrounds from a list of 10. How many combinations of backgrounds are possible?

  10. Your turn! Coach Hill randomly selects 3 people out of his class of 20 to go to the courts and help him get ready for a tennis match. How many possibilities of people does he have?

  11. Permutations & CombinationsReview • How many ways can we select 5 objects from a group of 20? • Does order matter? • If it does (maybe we are filling specific positions on a team), we have a permutation problem. How many? • If order does not matter (maybe we just want 5 different pieces of fruit) we have a combination problem. How many?

  12. Math I Today’s Question: How can we find the number of ways to select 9 people out of 20 for a party? There are 167960 different combinations of people.

  13. Class work • 349, # 1 – 21 all

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