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COUNTING PRINCIPLE

COUNTING PRINCIPLE. SIMULTANEOUS OUTCOMES. LET’S DO LUNCH!. You are choosing items at the deli for a sandwich. T urkey or h am, w heat or r ye, l ettuce or s prouts. Possible sandwich combinations are Twl, Tws, Trl, Trs, hwl, hws, hrl, hrs = 8

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COUNTING PRINCIPLE

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  1. COUNTING PRINCIPLE SIMULTANEOUS OUTCOMES

  2. LET’S DO LUNCH! • You are choosing items at the deli for a sandwich. Turkey or ham, wheat or rye, lettuce or sprouts. Possible sandwich combinations are Twl, Tws, Trl, Trs, hwl, hws, hrl, hrs = 8 Categories are: meat AND bread AND vegetable. Picking one from each kind and finding the total combinations applies the “counting principle”.

  3. The Formula • Counting Principle Formula: If there are m ways to choose from one kind and n ways to choose from another kind then there are m •n total possible outcomes. EX: 2 kinds of meat ·2 kinds of bread ∙2 kinds of vegetable = 8 total sandwiches Note: The formula applies to any number of categories/events

  4. Why Does It Work? • The “tree” diagram illustrates the principle: As the number of kinds are added, outcomes multiply! LETTUCE WHEAT SPROUTS TURKEY RYE LETTUCE SPROUTS LETTUCE WHEAT SPROUTS HAM LETTUCE RYE SPROUTS

  5. You Try! • How many six-symbol license plates (letters and digits) can be made if the first three are digits and the last three symbols are letters? __·__ ∙__ ·__ ∙__ ·__ (hint follows) Hint: multiply the number of choices of each symbol and note that any symbols may be repeated! (answer follows) ANSWER: 17,576,000 → (10·10∙10·26∙26·26)

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