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1 basic counting

  1. 1. BASIC COUNTING Counting is used to determine the number of these object
  2. 2. Basic counting rule Product and Sum Rule Product Rule • A count decomposes into a sequence of dependent counts (“each element in the first count is associated with all elements of the second count”)
  3. 3. example • assume an auditorium with a seat labeled by a letter and numbers in between 1 to 50. We want the total number of seats in the auditorium. HOW TO COUNT A-1 A-2 A-3 …A-50 B-1… Z-49 Z-50
  4. 4. 26 letters and 50 numbers. For each letter there are 50 numbers
  5. 5. So the number of seats is 26*50 = 1300 Product rule: number of letters * number of integers
  6. 6. TREE DIAGRAM Three officers - a president, a treasurer, and a secretary - are to be chosen from among four people: Ann, Bob, Clyde, and Dan. Suppose that for various reasons, Ann cannot be the president and either Clyde or Dan must be the secretary. In how many ways can the officers be chosen?
  7. 7. SUM RULE A count decomposes into a set of independent counts • “elements of counts are alternatives”, they do not depend on each other
  8. 8. Example: • You need to travel in between city A and B. You can either fly, take a train, or a bus. There are 12 different flights in between A and B, 5 different trains and 10 buses. How many options do you have to get from A to B?
  9. 9. • n = 12+5+10 Sum rule: • n = number of flights + number of trains + number of buses

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