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HorseCrazyGirlForever Group Title

When Andy is wiring a house, he must know if the customer has a gas or electric dryer, gas or electric furnace, & gas or electric water heater. How many different wiring combinations are possible for the dryer, furnace, and water heater? In addition to the above wiring combinations, Andy's customers have 3 choices for ceiling lighting. How many wiring combinations are possible for the dryer, furnace, water heater, & ceiling lighting?

  • one year ago
  • one year ago

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  1. tcarroll010 Group Title
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    Each appliance is independent of the other, so you merely multiply the number of choices available for each by the number of choices available for all the others. If you have n choices for the first and m choices for the second and o for the third and p for the fourth, then you have: m x n x o x p

    • one year ago
  2. tcarroll010 Group Title
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    So, to start, how many choices are available for the dryer, which is the first listed appliance?

    • one year ago
  3. HorseCrazyGirlForever Group Title
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    2

    • one year ago
  4. tcarroll010 Group Title
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    Good, and it looks like that is the same # for the furnace and the water heater. We have 3 different options for the ceiling lighting. So, just multiply those four numbers.

    • one year ago
  5. HorseCrazyGirlForever Group Title
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    So I would do 2x2x2x2?

    • one year ago
  6. tcarroll010 Group Title
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    Remember, the ceiling lighting has 3 options, so that last factor is not 2, it's 3.

    • one year ago
  7. HorseCrazyGirlForever Group Title
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    oh, I forgot to mention. The ceiling thing is not really connected to the first question.

    • one year ago
  8. tcarroll010 Group Title
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    That last question in the problem statement lists all four together, dryer, furnace, water heater, and ceiling lighting. So are you sure they are not related?

    • one year ago
  9. HorseCrazyGirlForever Group Title
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    They're connected, but they want the answer to this first:When Andy is wiring a house, he must know if the customer has a gas or electric dryer, gas or electric furnace, & gas or electric water heater. How many different wiring combinations are possible for the dryer, furnace, and water heater? Sorry for the confusion. :$

    • one year ago
  10. tcarroll010 Group Title
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    np. Then since each of the 3 appliances has 2 different ways of being wired, your answer is "2" multiplied by itself in number of times of the number of appliances.

    • one year ago
  11. tcarroll010 Group Title
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    This is usually expressed as:\[2^{n}\]where "n" is the number of objects.

    • one year ago
  12. HorseCrazyGirlForever Group Title
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    So the answer is 16

    • one year ago
  13. tcarroll010 Group Title
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    There are 3 appliances, so you are looking at:\[2^{3}\] which is not 16.

    • one year ago
  14. HorseCrazyGirlForever Group Title
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    8?

    • one year ago
  15. tcarroll010 Group Title
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    Perhaps you might want to be a little more confident about 8. It is definitely 8. Don't be afraid of the numbers. 2 x 2 x 2 is (2 x 2) x 2 is 4 x 2. That should give you a little more sureness about it.

    • one year ago
  16. HorseCrazyGirlForever Group Title
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    Yeah everyone else says that to... :/ Is that for the first half of the problem, or the ceiling one?

    • one year ago
  17. tcarroll010 Group Title
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    If you then take that number 8 into relation with the ceiling lighting, then you have 8 x 3 = 24. That's the same as what I originally proposed: 2 x 2 x 2 x 3

    • one year ago
  18. HorseCrazyGirlForever Group Title
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    Ohhh I see now! :) Thank you SO much for all your help! :D

    • one year ago
  19. tcarroll010 Group Title
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    You are very welcome!

    • one year ago
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