License plates in a particular state display 2 letters by 2

License plates in a particular state display 2 letters by 2 numbers. How many different license plates can be manufactured? (Repetitions are NOT allowed in the letter but are allowed in the numbers.) Do not enter commas or decimals in your answer. _____

Solution

There are 26 letters and 10 digits and 4 positions to fill.

Two letters (assuming repetition allowed) = 26*26 or 26^2=676
Two digits (assuming repetition is alllwed)= 10*10 =100
so number of plates with 2 letters followed by 2 digtis = 26^2 * 10^2=67,600