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Combinatorics

Combinatorics. Probability Unit M408 Trig/ PreCalc. Probability – The chance that particular random events will occur. Before we get to probability, we have to acquire some tools and definitions to help us with our calculations.

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Combinatorics

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  1. Combinatorics Probability Unit M408 Trig/PreCalc

  2. Probability – The chance that particular random events will occur. • Before we get to probability, we have to acquire some tools and definitions to help us with our calculations. • Combinatorics – involves counting possible arrangements of large numbers of objects. • Independent Events – These events do not affect or relate to each other. • Dependent Events – These events are related, and can affect each other.

  3. Basic Counting Principle (Slot Method) • Only used with Independent Events • Used to count the total number of ways for multiple events to occur at the same time. • Involves simply multiplying the number of possible outcomes of each independent event.

  4. Example 1 • I have 6 flavors of yogurt, 4 types of granola bars, and 5 different juices to choose from. How many different healthy breakfasts options are there if I choose one of each?

  5. Example 2 – How many different license plates could be made with… • A.) 2 letters, the first of which is Q, followed by 3 digits, with no repetition of letters or digits? • B.) 2 letters, followed by a 4 digit even number with repetition allowed? • C.) 2 Letters followed by a 4 digit even number with no repetition allowed?

  6. Example 3 • How many three digit even numbers could you form with {0,1,2,3,4} with no repeat digits?

  7. Example 4 • There are 10 competitors in the dance-off. How many ways could you award 1st, 2nd, and 3rd place?

  8. Example 5 • How many ways are there to line up 8 students?

  9. Factorials: n! = n(n-1)(n-2)…(2)(1) Example 6 – a.) 8! b.) 5! c.) 20! d.) 1! e.) 0! n! = n(n-1)(n-2)…(2)(1) (n-1)! = (n-1)(n-2)…(2)(1) So Now plug in n = 1.

  10. Example 7 - Simplify a.) b.) c.) d.)

  11. Example 8 - Simplify

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