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The multiplication Counting Principle

The multiplication Counting Principle. Lesson 2.9. Getting Started…. Answer true or false for 1–4. You may have to guess. 1 . The unit of money in Mauritius is the rupee. 2. The Prime Minister of Canada in 1900 was Laurier. 3. Stan Jok played baseball for the Boston Red Sox.

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The multiplication Counting Principle

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  1. The multiplication Counting Principle Lesson 2.9

  2. Getting Started… • Answer true or false for 1–4. You may have to guess. • 1. The unit of money in Mauritius is the rupee. • 2. The Prime Minister of Canada in 1900 was Laurier. • 3. Stan Jok played baseball for the Boston Red Sox. • 4. Hannah Van Buren’s maiden name was Hoes. • 5. List all the possible ways to answer the four questions. How many possibilities are there?

  3. Multiplication Counting Principle • If one choice can be made in m ways and a second choice can be made in n ways, then there are mn ways of making the first choice followed by the second choice.

  4. Example 1 , p. 119 • Suppose a stadium has 9 gates. Gates A, B, C, and D are on the north side, and gates E, F, G, H, and I are on the south side. In how many ways can you enter the stadium through a north gate and leave through a south gate? Gates Of Exit Gates Of entry

  5. Coin Flip • A coin is tossed in the air 3 times. How many different combinations could be created? Method 1: HHH THH TTH TTT HTH THT HHT HTT

  6. A coin is tossed in the air 3 times. How many different combinations could be created? Method 2: H T H H H T T H H T H T T T

  7. Example 2, p. 120 • A high-school student wants to take a foreign-language class, a music course, and an art course. The language classes available are French, Spanish, and German. The music classes available are chorus and band. The art classes available are drawing and painting. In how many different ways can the student choose the three classes?

  8. Method 1: • F – C – P G – C – P S – C – P • F – C – D G – C – D S – C - D • F – B – P G – B – P S – B - P • F – B – D G – B – D S – B – D 12 possibilities!

  9. Method 2: drawing painting chorus drawing Spanish band painting drawing painting chorus drawing French band painting drawing chorus painting German drawing band painting

  10. Method 3: 3 2 2 • • (ways to choose A language) (ways to choose a music) (ways to choose an art) There are 12 ways to choose classes.

  11. Example 3, p. 121 • Miss Helbing is giving her algebra class a quiz with 5 questions. Since Angela has not done her homework, she has to guess. The quiz has two multiple-choice questions with choices A, B, C, and D and three true – false questions. • A.) how many possible ways are there for Angela to answer all 5 questions? 4 4 2 2 2 • • • • = 128

  12. What is the probability that Angela will get all of the questions correct? 1 128

  13. Example 4, p. 121 • Mr. Roberts has written a chapter test. It has three multiple choice questions each with m possible answers, two multiple-choice questions each with n possible answers, and 5 true-false questions. How many ways are there to answer the questions? • • m m m • n • n • 2 • 2 • 2 • 2 • 2 32m3n2

  14. Homework: • Page 122 – 123 10 - 17

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