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September 27th, 2017, 02:44 AM  #1 
Newbie Joined: Sep 2017 From: Saudi Arabia Posts: 20 Thanks: 1  Calculating the number of ways
How many codes can we create if we have to follow the conditions: * Exactly two distinct numbers (09) must be used. * Exactly two distinct letters (AZ) must be used. * The dot symbol (.) must be used exactly one time. * The number zero (0) must not be in the leftmost position. * The dot symbol (.) must not be in the leftmost position nor the rightmost position. 
September 27th, 2017, 03:09 AM  #2  
Senior Member Joined: Feb 2016 From: Australia Posts: 1,453 Thanks: 489 Math Focus: Yet to find out.  Quote:
 
September 27th, 2017, 05:01 AM  #3 
Newbie Joined: Sep 2017 From: Saudi Arabia Posts: 20 Thanks: 1  
September 27th, 2017, 06:36 AM  #4 
Math Team Joined: Jul 2013 From: काठमाडौं, नेपाल Posts: 872 Thanks: 60 Math Focus: सामान्य गणित 
Can you give examples of such codes? And what is the required length of the codes?

September 27th, 2017, 08:57 AM  #5 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 11,064 Thanks: 722 
Looks to me like length always = 5, "lowest" code being 1.0AB "highest" being 9.8YZ 
September 27th, 2017, 01:38 PM  #6 
Newbie Joined: Sep 2017 From: Saudi Arabia Posts: 20 Thanks: 1  
September 27th, 2017, 01:40 PM  #7 
Newbie Joined: Sep 2017 From: Saudi Arabia Posts: 20 Thanks: 1  
September 28th, 2017, 06:31 AM  #8 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 11,064 Thanks: 722 
Well, keep it simple. Forget the "." Calculate arrangements with 10 digits and 26 letters, with exception being 9 digits in leftmost position. Then multiply result by 3, since "." can only fit in 3 places. As Grouchy Sir Joppy said: we don't give full solutions... 

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