A valid license plate in Xanadu consists of two letters followed by three digits. How many valid license plates are possible?

As long as repeats are allowed, the number possible  is (26)(26)*10^3 = 676,000

lets pretend that letters and numbers are the same things. so we have got 1234567890 and lets call the letters just capital letters instead so all the numbers are 1234567890ABCDEFGHIJKLMNOPQRSTUVWXYZ. the number plate is a bit like a combinatiobn lock (think about it) and the formula for the number of possible permutaions on a combination lock ( it should be could a permutation lock i don't know why it's called combonation lock ) is:

(amount of different numbers)^{(how many digits wide the lock is)}

so we replace amount of different numbers with 36 and how many digits wide the lock is with 5 to get 36⁵ = 60,466,176

so there you go.

Scruffy23:

You are all confused. Look carefully at the question which says " consists of two letters followed by three digits". Example: AA111, if repeats are allowed. So, starting from the left: You can choose A out of 26 letters. The same with the second A from the left. Then, starting with 1, you have 10 choices from 0 - 9 to choose from. The same with the second and third 1's. So, as CPhill calculated, you have a total of: 26 x 26 x10 x10 x10 =676,000!!.