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LyraElizabethAdams Group Title

I need some help, please! :) . . . "Explain why the following sentences are INCORRECT: John has 3 suits, 10 shirts, and 12 neckties.  He will need to buy some more clothes if he wants to come to work each work day in a different outfit for a whole year."

  • 2 years ago
  • 2 years ago

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  1. wio Group Title
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    We can assume that an outfit would just be the combination of a suit, shirt, and necktie. When tasks are done in parallel (you must do one task or the other), then their sum is the total number of combinations. When tasks are done in sequence (you must do all tasks), then their product is the total number of combinations.

    • 2 years ago
  2. wio Group Title
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    In this case, it is a sequence of tasks. So we multiply the number of ways to do the task.

    • 2 years ago
  3. wio Group Title
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    The only ambiguity here is if he can go to work without a tie, shirt, or suit. In that case, we could add 1 to each task.

    • 2 years ago
  4. LyraElizabethAdams Group Title
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    Okay, I do understand that part. Here's where I'm confused, though. Should I do: (3)(10)(12) = 360? or should it be 360C3 (because you have a total of 360 choices, but you can only choose 3 per day?

    • 2 years ago
  5. wio Group Title
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    It is NOT 360 choose 3. We would use 360 choose 3 if he had 360 articles of clothing, and any combination of 3 articles is an outfit.

    • 2 years ago
  6. LyraElizabethAdams Group Title
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    Why doesn't John choose 3?

    • 2 years ago
  7. wio Group Title
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    Because he can't do something like wear 3 shirts and call that an outfit.

    • 2 years ago
  8. LyraElizabethAdams Group Title
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    Oh, I see. Oh, so should I do either 25C3 or 25P3 ?

    • 2 years ago
  9. wio Group Title
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    No, it is not a complicated problem like that. It's just multiplication.

    • 2 years ago
  10. LyraElizabethAdams Group Title
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    Oh, okay. So just (3)(10)(12) = 360 ?

    • 2 years ago
  11. wio Group Title
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    The only detail that is important is if he can do something like NOT wear a necktie or NOT wear a suit.

    • 2 years ago
  12. wio Group Title
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    because that would mean we'd have something like (3+1)(10+1)(12+1)

    • 2 years ago
  13. LyraElizabethAdams Group Title
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    Okay, I'll remember that.

    • 2 years ago
  14. wio Group Title
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    But if he must have all three, then yes, 360 is correct.

    • 2 years ago
  15. LyraElizabethAdams Group Title
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    Okay, great - thanks so much! :D

    • 2 years ago
  16. campbell_st Group Title
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    ok by the fundamental theorem of counting John has 3 x 10 x 12 = 360 possible clothing combinations... assuming he works 365 days a year he is 5 combinations short...

    • 2 years ago
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