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?
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