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3.4A-Fundamental Counting Principle

3.4A-Fundamental Counting Principle. The number of ways 2 events can occur in sequence (1 after the other) is m x n and it can be extended for more events.

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3.4A-Fundamental Counting Principle

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  1. 3.4A-Fundamental Counting Principle • The number of ways 2 events can occur in sequence (1 after the other) is m x n and it can be extended for more events. • Example: You buy a car. The dealer carries: 3 brands (Ford, GM, and Chrysler) in 2 sizes (small & medium)and in 4 colors(white, red, black & green). How many options do you have? Make a tree diagram. • If the dealer added Toyota, Large, Tan and Gray to the previous options, how many are there?

  2. 3.4A-Fundamental Counting Principle • The number of ways 2 events can occur in sequence (1 after the other) is m x n and it can be extended for more events. • Example: You buy a car. The dealer carries: 3 brands (Ford, GM, and Chrysler) in 2 sizes (small & medium)and in 4 colors(white, red, black & green). How many options do you have? Make a tree diagram. • 3x2x4 = 24 options Ford GM Chrysler S M S M S M W R B G W R B G W R B G W R B G W R B G W R B G

  3. 3.4A-Fundamental Counting Principle • The number of ways 2 events can occur in sequence (1 after the other) is m x n and it can be extended for more events. • Example: You buy a car. The dealer carries: 3 brands (Ford, GM, and Chrysler) in 2 sizes (small & medium)and in 4 colors(white, red, black & green). How many options do you have? Make a tree diagram. • If the dealer added Toyota, Large, Tan and Gray to the previous options, how many are there? 4x3x6 = 72

  4. More examples • A car access code has 4 digits (0-9). How many codes are possible if: • A) each can be used just once (NO REPEATS!) • B) each digit CAN REPEAT

  5. More examples • A car access code has 4 digits (0-9). How many codes are possible if: • A) each can be used just once (NO REPEATS!) 10x9x8x7=5040 • B) each digit CAN REPEAT

  6. More examples • A car access code has 4 digits (0-9). How many codes are possible if: • A) each can be used just once (NO REPEATS!) 10x9x8x7=5040 • B) each digit CAN REPEAT 10x10x10x10 = 10,000

  7. More examples • How many license plates can be made if each plate has 6 letters (there are 26 possible) and: • A) repeated letters are allowed • B) No repeats of letters

  8. More examples • How many license plates can be made if each plate has 6 letters (there are 26 possible) and: • A) repeated letters are allowed 26x26x26x26x26x26 =308,915,776 • B) No repeats of letters

  9. More examples • How many license plates can be made if each plate has 6 letters (there are 26 possible) and: • A) repeated letters are allowed 26x26x26x26x26x26 =308,915,776 • B) No repeats of letters 26x25x24x23x22x21 = 165,765,600

  10. More examples • How many different ways can you flip a coin, roll a 6-sided die and answer a true/false question? • Draw a tree diagram for it.

  11. More examples • How many different ways can you flip a coin, roll a 6-sided die and answer a true/false question? 2x6x2 = 24 • Draw a tree diagram for it.

  12. More examples • How many different ways can you flip a coin, roll a 6-sided die and answer a true/false question? 2x6x2= 24 • Draw a tree diagram for it. H T 1 2 3 4 5 6 1 2 3 4 5 6 T F T F T F T F T F T F T F T F T F T F T F T F

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