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# 10x9x8x7x6x5x4 Description

##### Description: These are examples of the material that is on the exam. Some are re-worked examples we got in class
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Exam 2 Wednesday,  October 19, 2016 11:53 AMContents: - Counting and tree diagrams - Rearrangements  - probability Counting and tree diagrams: Suppose that you have the set S= {1,2,3,4} How many 3 element subsets can one create? A: 4  Use a tree diagram  Levels represent a selection round Leaves represent an outcome  Since we don’t care about the order you don't count all  the leaves (the definition of a subset is that the elements  are the same no matter the order. Ex. 1234 and 2314) With bigger alphabets you can figure out the  answer by taking the number of total  rearrangements and dividing it by the number of  nce we on care aou e orer you on coun a  the leaves (the definition of a subset is that the elements  are the same no matter the order. Ex. 1234 and 2314) With bigger alphabets you can figure out the  answer by taking the number of total  rearrangements and dividing it by the number of  subsets.  Ex. If you have the alphabet  {0,1,2,3,4,5,6,7,8,9} and you want to find the  number of 4 element subsets that can be  created with that set: First: there are 10x9x8x7 possible 4  element arrangements Then figure out that there are 24  possible subsets because 1 subset  contains 4 elements that can be  arranged 4! Ways Now let's try a harder example:How many codes of length 7 can you create using the  alphabet {0,1,2,3,4,5,6,7,8,9} (repeated digits allowed) First  Step: Determine the size of your alphabet  You have a 10 digit alphabet

Step two: Determine how many levels of the tree you will have  You have 7 choices for each digit  in the code. Raise 10 to the 7th because you  have 5 choices

## How many 3 element subsets can one create?

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