Electrical Switches, pls help !!

talhakosen · 2009-11-01 05:39:03

how many different ways you can connect five switches, using four wires.

Last edited by talhakosen (2009-11-04 08:31:38)

bobbym · 2009-11-01 10:15:12

Hi talhakosen;

I can't see the figure. The question is too ambiguous for me without it.

Last edited by bobbym (2009-11-01 11:10:11)

talhakosen · 2009-11-01 23:22:08

Please look at this picture

Last edited by talhakosen (2009-11-03 00:30:07)

mathsyperson · 2009-11-02 00:02:38

The only way that a set of four wires won't connect all of the switches, is if three or four of them form a loop.

I'd say it's best to count the number of ways that can be done, and take that number away from the total amount of possible combinations.

I get an answer of 210 - 70 - 5 = 135.

talhakosen · 2009-11-02 03:27:55

Thanks for giving your time !

talhakosen · 2009-11-02 16:54:59

Hi mathsyperson,

210 - 70 - 5 = 135.
i really tought about the number that you . But i couldnt understood how to find them clearly. Could you please give me more info ?
Thanks a lot

mathsyperson · 2009-11-02 23:00:56

I had another think about this when I couldn't get the numbers to add up, and it turns out that there are actually 15 types of 4-loops, not 5. That makes the actual answer 125.

Here's a breakdown of the different types of connections:

i) The four wires form a continuous path, with no branches. Your second picture is an example of this.
There are 5!/2 = 60 ways of making this type of connection.

ii) One of the switches has three wires connected to it, and one of those wires is twice as long as the others.
There are 5*4*3 = 60 ways of doing this.

iii) One of the switches has all four wires connected to it, like in your first picture.
There are 5 ways of doing this.

---

iv) Three of the wires form a triangle.
There are 5C3 * 7 = 70 ways of doing this.

v) The four wires form a loop.
There are 5!/(4*2) = 15 ways of doing this.

These all add up to 210 = 10C4, which means all possible placements have been accounted for.
You're interested in the top three types, so your answer is 60+60+5 = 125.

talhakosen · 2009-11-03 00:29:45

firs of all thanks for you answer mathsyperson ! It is really awesome...

5C3 * 7 , i understood it 7 comes from free wire, (AE,AD,BE,BD,CE,CD,DE)

but i couldnt see how 4 wires form can be 15 times in switches.
i can think only 5c4 !!
Could you explain it to me if you have a little time more ...

mathsyperson · 2009-11-03 02:35:25

That's where I originally got the 5 from too, but that only considers the vertices used, and not the order.

If the loop was made on switches A, B, C and D, the order could be:

ABCDA
ABDCA
ACBDA

And so we need to multiply the 5C4 by 3 to get the right answer.

talhakosen · 2009-11-03 03:16:15

i see now thanks a lot

Math Is Fun Forum

#1 2009-11-01 05:39:03

Electrical Switches, pls help !!

#2 2009-11-01 10:15:12

Re: Electrical Switches, pls help !!

#3 2009-11-01 23:22:08

Re: Electrical Switches, pls help !!

#4 2009-11-02 00:02:38

Re: Electrical Switches, pls help !!

#5 2009-11-02 03:27:55

Re: Electrical Switches, pls help !!

#6 2009-11-02 16:54:59

Re: Electrical Switches, pls help !!

#7 2009-11-02 23:00:56

Re: Electrical Switches, pls help !!

#8 2009-11-03 00:29:45

Re: Electrical Switches, pls help !!

#9 2009-11-03 02:35:25

Re: Electrical Switches, pls help !!

#10 2009-11-03 03:16:15

Re: Electrical Switches, pls help !!

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