Counting examples

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Counting examples

  1. 1. Counting Examples Mathematics 4 February 14, 2012Mathematics 4 () Counting Examples February 14, 2012 1 / 13
  2. 2. Fundamental Counting PrincipleIf one event can be done independently n different ways and a secondevent can be done independently m different ways, the total number ofways all things may be done in the stated order is n · m. Mathematics 4 () Counting Examples February 14, 2012 2 / 13
  3. 3. Example 1 How many three-digit numbers can be formed from the digits 1, 2, 3, 4, and 5 if repetitions are allowed? If repetitions are not allowed? Mathematics 4 () Counting Examples February 14, 2012 3 / 13
  4. 4. Example 2 How many numbers can be formed from the digits 1, 2, 3, 4, and 5 if repetitions are not allowed? (1 to 54321) Mathematics 4 () Counting Examples February 14, 2012 4 / 13
  5. 5. Example 3If eight basketball teams are in a tournament, find the number of different ways that first, second, and third place can be decided, assuming ties are not allowed. Mathematics 4 () Counting Examples February 14, 2012 5 / 13
  6. 6. Example 4A girl has four skirts, six blouses, and three sweaters. How many different skirt-blouse-sweater combinations can she wear? Mathematics 4 () Counting Examples February 14, 2012 6 / 13
  7. 7. Example 5Automobile license plates start with three letters of the alphabet, followed by three digits. Find how many different license plates are possible if 1 the first digit following the last letter cannot be 0 Mathematics 4 () Counting Examples February 14, 2012 7 / 13
  8. 8. Example 5Automobile license plates start with three letters of the alphabet, followed by three digits. Find how many different license plates are possible if 1 the first digit following the last letter cannot be 0 2 the first letter cannot be I or O and the first digit cannot be 0 Mathematics 4 () Counting Examples February 14, 2012 7 / 13
  9. 9. Example 6Two diced are tossed, one after the other. In how many different ways can they fall? Mathematics 4 () Counting Examples February 14, 2012 8 / 13
  10. 10. Example 7 Two diced are tossed, one after the other. How many different ways can the sum of the dots equal 1 3 Mathematics 4 () Counting Examples February 14, 2012 9 / 13
  11. 11. Example 7 Two diced are tossed, one after the other. How many different ways can the sum of the dots equal 1 3 2 5 Mathematics 4 () Counting Examples February 14, 2012 9 / 13
  12. 12. Example 7 Two diced are tossed, one after the other. How many different ways can the sum of the dots equal 1 3 2 5 3 7 Mathematics 4 () Counting Examples February 14, 2012 9 / 13
  13. 13. Example 7 Two diced are tossed, one after the other. How many different ways can the sum of the dots equal 1 3 2 5 3 7 4 9 Mathematics 4 () Counting Examples February 14, 2012 9 / 13
  14. 14. Example 7 Two diced are tossed, one after the other. How many different ways can the sum of the dots equal 1 3 2 5 3 7 4 9 5 11 Mathematics 4 () Counting Examples February 14, 2012 9 / 13
  15. 15. Example 8 A row of six seats in a classroom is to be filled by selecting individuals from a group of six boys and four girls. If boys and girls are to be alternated, find the number of different seating arrangements. Mathematics 4 () Counting Examples February 14, 2012 10 / 13
  16. 16. Example 9In how many ways can a test consisting of ten true-or-false questions can be completed? Mathematics 4 () Counting Examples February 14, 2012 11 / 13
  17. 17. Example 10 A test consists of six multiple-choice questions, and there are five choicesfor each question. In how many different ways can the test be completed? Mathematics 4 () Counting Examples February 14, 2012 12 / 13
  18. 18. Example 11 Three high-school couples have purchased movie tickets. Partners are tobe seated next to each other, and the six seats are in a row. In how many ways can the six people be seated? Mathematics 4 () Counting Examples February 14, 2012 13 / 13
  19. 19. Example 12 In how many ways can a standard deck of cards be shuffled so that the four aces appear on the top of the deck? Mathematics 4 () Counting Examples February 14, 2012 14 / 13
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