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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 (0-9) must be used. * Exactly two distinct letters (A-Z) 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
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Quote:
 Originally Posted by Hussain2629 How many codes can we create if we have to follow the conditions: * Exactly two distinct numbers (0-9) must be used. * Exactly two distinct letters (A-Z) 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.
What have you tried? Can you determine the number of ways given just one of those conditions?

September 27th, 2017, 05:01 AM   #3
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Quote:
 Originally Posted by Joppy What have you tried? Can you determine the number of ways given just one of those conditions?
Actually, I could not begin to solve this problem.

 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
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Quote:
 Originally Posted by MATHEMATICIAN Can you give examples of such codes? And what is the required length of the codes?
If you read it carefully, you will see that the length = 5

Some examples: h.2c9
5c.2k
94y.s

September 27th, 2017, 01:40 PM   #7
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 Originally Posted by Denis Looks to me like length always = 5, "lowest" code being 1.0AB "highest" being 9.8YZ
The dot symbol can be used between the letters as well

Such as w.k27

 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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