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jmc

counting and probability senior

Problem

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?
problem
Solution
There are 26 ways to choose the repeated letter, ways to choose the other two letters, ways to choose in which two of the four positions to put the repeated letters, 2 ways to choose how to arrange the remaining two letters, 10 ways to choose the first digit and 9 ways to choose the second digit for a total of combinations.
Final answer
8,\!424,\!000