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Counting Techniques

Counting Techniques. 3.6. How many 2 digit numbers can you make when selecting odd digits?. Fundamental Counting Rule. For a sequence of events in which the first can occur in m ways and the 2 nd can occur in n ways, the events together can occur a total of m∙n ways.

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Counting Techniques

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  1. Counting Techniques 3.6

  2. How many 2 digit numbers can you make when selecting odd digits?

  3. Fundamental Counting Rule • For a sequence of events in which the first can occur in m ways and the 2nd can occur in n ways, the events together can occur a total of m∙n ways. • Ex) A code is made from choosing a letter followed by a digit. How many possible codes can you make?

  4. Computer design • In computer designing a byte is defined to be a sequence of 8 bits and each bit can be a 0 or a 1. How many different bytes are possible? (a example of a byte is 01000001=letter A)

  5. Factorial • Factorial Symbol – ! Is the factorial symbol. Use this when you are choosing from n items arranged in n different ways. • 4! = 4 x 3 x 2 x 1 = 24 • 0! = 1 by rule • Can find the factorial sign under MATH/PROB on a graphing calculator. Ex) On a basketball team there are 5 positions. How many ways can we create a starting lineup from 5 people?

  6. Jimbo is taking AP Lit, U.S. History, and Calculus. How many possible ways can Jimbo’s schedule be ordered?

  7. Day 2 • Permutations: The number of permutations of r items selected from n available items (without replacement) is • Order makes a difference… ac and ca are different • Find it on your calcMATH/PROB/nPr • Have to enter the n-value 1st

  8. Permutation example • Frank Sinatra recorded 381 songs. Rolling Stone Magazine wants to put together a top ten list. How many different top 10 lists can they make?

  9. Examples • How many different “words” can be created from the letters SADLER? • A student council of 18 has 8 girls. How may different ways can we pick a president, vice president, and treasurer? • How many ways can we elect just boys?

  10. Permutation with repetition • IF there are n items with alike items, alike items,…, alike items the number of permutations of the n items is • Ex) How many different “words” can you create from the letters AABBBBCCD?

  11. Day 3 Combination Rule • The number of combinations of r items selected from n different items is • Order doesn’t matter ac and ca are the same. • On CalcMATH/PROB/nCr

  12. Combination example • A board of trustees has nine members. A subcommittee must be formed to decide a scholarship winner. How many different groups can be formed? • The board also must elect a President and a Vice President. How many ways can they do that?

  13. Lotto • The New York State lottery has a game where a player chooses 6 numbers out of a possible 51. To win the jackpot the player must have all six numbers. • How many different tickets can be formed? • What is the probability of winning?

  14. Cards • Select 5 cards. • How many different 5 card hands can you get? • How many ways can you get 5 spades? • What is the probability of getting 5 spades?

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