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Automobile license plates for a state consist of four letters followed by a dash and two single digits. How many different license plate combinations are possible if exactly one letter is repeated exactly once, but digits cannot be repeated?

 Apr 17, 2019
 #1
avatar+18360 
+1

(Deleted......see CPhill's answer) 

 Apr 17, 2019
edited by ElectricPavlov  Apr 17, 2019
 #2
avatar+100571 
+2

Here's my attempt

 

Possible letter combos

Choose any letter  and let this also be the repeated letter = 26 ways

But....we have 4C2 = 6  positions for the two identical letters to occupy.....

And we have (25)(24) ways to choose the other two letters

 

So...I believe that the total number of "words"  = 4C2 * 26 *25*24  = 93600

 

And since the digits cannot be repeated  = 10 * 9  =  90

 

So...the total possibilities  =  93600 * 90  =  8,424,000

 

 

cool cool cool

 Apr 17, 2019

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