anonymous
  • anonymous
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?
Mathematics
jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
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
anonymous
  • anonymous
So, to start, how many choices are available for the dryer, which is the first listed appliance?
anonymous
  • anonymous
2

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anonymous
  • anonymous
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.
anonymous
  • anonymous
So I would do 2x2x2x2?
anonymous
  • anonymous
Remember, the ceiling lighting has 3 options, so that last factor is not 2, it's 3.
anonymous
  • anonymous
oh, I forgot to mention. The ceiling thing is not really connected to the first question.
anonymous
  • anonymous
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?
anonymous
  • anonymous
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. :$
anonymous
  • anonymous
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.
anonymous
  • anonymous
This is usually expressed as:\[2^{n}\]where "n" is the number of objects.
anonymous
  • anonymous
So the answer is 16
anonymous
  • anonymous
There are 3 appliances, so you are looking at:\[2^{3}\] which is not 16.
anonymous
  • anonymous
8?
anonymous
  • anonymous
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.
anonymous
  • anonymous
Yeah everyone else says that to... :/ Is that for the first half of the problem, or the ceiling one?
anonymous
  • anonymous
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
anonymous
  • anonymous
Ohhh I see now! :) Thank you SO much for all your help! :D
anonymous
  • anonymous
You are very welcome!

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