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April 1st, 2014, 06:20 PM  #1 
Newbie Joined: Apr 2014 From: Auckland Posts: 3 Thanks: 0  Telephone Network
Hi, Please help me with the following, im unsure how to write up the equation. Problem: Imagine a network of Telephones. There are 10 Telephones in the Network. Each Telephone is connected with a cable to each other Telephone. How many cables are there? And How many cables would you require for a network of 20 Telephones? Thanks. 
April 1st, 2014, 06:48 PM  #2 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,690 Thanks: 2669 Math Focus: Mainly analysis and algebra 
Start with one of the telephones. Count the cables you need to link it to the rest. Do the same for the second telephone bearing in mind that it is already linked to the first. Repeat for all telephones. 
April 1st, 2014, 07:48 PM  #3  
Senior Member Joined: Sep 2012 From: British Columbia, Canada Posts: 764 Thanks: 53  Quote:
Are you familiar with binomial coefficients? Since a cable connects two phones, and there are 10 of them, then there are 10C2 = 45 cables in total. With 20 phones, there are 20C2 cables in total.  
April 3rd, 2014, 06:08 AM  #4  
Member Joined: Jan 2014 From: Tashkent, Uzbekistan Posts: 52 Thanks: 2  Quote:
Formula for the number of diagonals: $\displaystyle \frac{n(n3)}{2}$ where n is the number of sides (or telephones) Last edited by sf7; April 3rd, 2014 at 06:11 AM.  
April 3rd, 2014, 06:09 AM  #5 
Member Joined: Jan 2014 From: Tashkent, Uzbekistan Posts: 52 Thanks: 2  eddybob123, could you explain in an example how it is calculated? Thanks in advance!

April 3rd, 2014, 04:41 PM  #6  
Newbie Joined: Apr 2014 From: Auckland Posts: 3 Thanks: 0  Quote:
 
April 4th, 2014, 11:23 AM  #7 
Global Moderator Joined: Dec 2006 Posts: 21,035 Thanks: 2271  

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