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Chapter 4.4

Chapter 4.4. FCP and factorials. Counting Rules. Counting rules are used to find the total number of possible outcomes Four major methods. Fundamental counting Principle.

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Chapter 4.4

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  1. Chapter 4.4 FCP and factorials

  2. Counting Rules • Counting rules are used to find the total number of possible outcomes • Four major methods

  3. Fundamental counting Principle • In a sequence of n events in which the first one has k1 possibilities and the second event has k2 possibilities and so forth, the total number of possibilities of the sequence will be k1*k2 * k3 ….. kn

  4. Pizza • Suppose that a pizzeria has a special for personal pizzas. A customer can choose one from each column. How many possible pizzas are there?

  5. Tossing a coin and Rolling a die • A coin is tossed and a die is rolled. Find the number of outcomes for the sequence of events.

  6. Types of Paint • A paint manufacturer wishes to manufacture several different paints. The categories include: How many different kinds of paint can be made if you can select one color, one type, one texture, and one use?

  7. Blood types • There are four blood types, A, B, AB, O. Blood can also be Rh+ and Rh-. Finally, a blood donor can be classified as either male or female. How many different ways can a donor have his or her blood labeled?

  8. Identification Cards • The manager of a department store chain wishes to make four-digit identification cards for her employees. How many different cards can be made if she uses the digits 1, 2, 3, 4, 5, 6 and repetitions are permitted?

  9. Pin Numbers • You are selecting a four digit pin number for your debit card. How many possible pin numbers are there if repetitions are permitted? If repetitions are not permitted?

  10. License plates • In the state of NJ, a license plate consists of 3 letters, followed by 2 digits, followed by a letter. How many possible license plates are there?

  11. Telephone numbers • Telephone numbers are made up of a 3 digit area code, followed by three digits called the exchange, followed by four digits called the subscriber number. 0 and 1 cannot be the first digit of the area code or the first digit of the exchange. The digits “555” cannot be the exchange. How many possible phone numbers are there?

  12. factorials • Factorials are used to find the number of arrangements that are possible. Order matters. All items in the set are being arranged • Factorial notation: n!

  13. Textbooks • How many ways can six textbooks be arranged on a shelf?

  14. Paintings • How many ways can 8 paintings be hung on a wall?

  15. Ducks in a row • How many ways can we line up in the front of the room?

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