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Chapter 10

Chapter 10. Counting Techniques. Sequential Counting Principle Section 10.1. Tree Diagrams. Tree Diagrams are used to display all the possible outcomes of a situation. H. H. T. H. T. T. Sequential Counting Principle. SCP

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Chapter 10

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  1. Chapter 10 Counting Techniques

  2. Sequential Counting PrincipleSection 10.1

  3. Tree Diagrams • Tree Diagrams are used to display all • the possible outcomes of a situation. • H • H T • H T T

  4. Sequential Counting Principle • SCP • If an event can occur in m ways and a second event can occur in n ways, then the sequence of two events can occur in m x n ways.

  5. SCP • Fundamental Counting Principle • If an event can occur in m ways, and then a second event can occur in n ways, and then a third event can occur in r ways, and so on, then the sequence of events can occur in mnr … ways.

  6. Exercise: • A bag contains 6 brown marbles and 3 white marbles. You are asked to draw 3 marbles from the bag without replacement. In how many ways can you draw 2 brown and 1 white in that order? 6 x 5 x 3 = 90 1st B 2nd B 1st W

  7. Exercise: In how many ways can 1 woman and 1 man, in that order, be selected from 5 women and 6 men? 5 x 6 = 30

  8. Exercise: How many different sets of 3 initials can be made from the letters of the English alphabet? Hint: AAA is different from BBB. 26 x 26 x 26 = 17,576

  9. Exercise: The Good Taste Restaurant has 7 entrees, 6 vegetables, and 9 desserts on its menu. If you want to order 1 entree, 1 vegetable, and 1 dessert, how many choices do you have? 7 x 6 x 9 = 378

  10. Exercise: In Connecticut, auto license plates carry 3 digits followed by 3 letters. a. How many arrangements are possible for the 3 letters? b. How many arrangements are possible for the 3 numbers? c. How many different license plates can be made using 3 numbers followed by 3 letters? a. 26 x 26 x 26 = 17,576 b. 10 x 10 x 10 = 1000 c. 17,576 x 1000 = 17,576,000

  11. Exercise: Social Security numbers consist of nine digits. a. If the first digit cannot be a 0, how many Social Security numbers are possible? b.How many Social Security numbers are possible if there are no restrictions? 9 10 10 10 10 10 10 10 10  9 x 108 = 900,000,000 10 10 10 10 10 10 10 10 10  109 = 1,000,000,000

  12. DICE

  13. You are expected to be familiar with a standard deck of playing cards.

  14. Note: the Ace will be considered to be a one. There are four suits: Clubs, Diamonds, Spades, and Hearts in a deck of cards. END

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