Question

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?

Answer 1

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

Answer 2

So, to start, how many choices are available for the dryer, which is the first listed appliance?

Answer 3

2

Answer 4

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.

Answer 5

So I would do 2x2x2x2?

Answer 6

Remember, the ceiling lighting has 3 options, so that last factor is not 2, it's 3.

Answer 7

oh, I forgot to mention. The ceiling thing is not really connected to the first question.

Answer 8

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?

Answer 9

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. :$

Answer 10

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.

Answer 11

This is usually expressed as:\[2^{n}\]where "n" is the number of objects.

Answer 12

So the answer is 16

Answer 13

There are 3 appliances, so you are looking at:\[2^{3}\] which is not 16.

Answer 14

8?

Answer 15

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.

Answer 16

Yeah everyone else says that to... :/ Is that for the first half of the problem, or the ceiling one?

Answer 17

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

Answer 18

Ohhh I see now! :) Thank you SO much for all your help! :D

Answer 19

You are very welcome!