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March 19th, 2018, 09:54 PM  #1 
Newbie Joined: Sep 2017 From: Saudi Arabia Posts: 29 Thanks: 1  How many codes can we create? Hi all, can you please help me to find out the number of codes? 
March 20th, 2018, 03:04 AM  #2 
Senior Member Joined: Feb 2010 Posts: 682 Thanks: 129 
I'll take a stab at this. 3 places for the dot, $\displaystyle \binom{26}{2}$ ways to choose two letters, $\displaystyle \binom{10}{2}$ ways to choose two numbers, and 4! ways to line them up gives all ways allowing a zero at the start. So now we subtract out all those with zero at the start. Again, 3 places for the dot, $\displaystyle \binom{26}{2}$ ways to choose two letters, 9 ways to choose a digit, and 3! ways to line them up. So, $\displaystyle 3 \cdot \binom{26}{2}\binom{10}{2} \cdot 4!  3 \cdot \binom{26}{2}\binom{9}{1} \cdot 3! = 100350$ 

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