The license plates
In Italy we have a characteristic sistem of license plates. The structure of the plates is the following:
So, you can see that there are 2 letters, 3 digits and other 2 letters. If we use the whole alphabet (26 letters) add all the digits (10), how many plates we can make with this sistem?
(A letter or a digit can be repeated)
- image rights: Targheshop
The answer is 456976000.
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1 solution
We know that we can use 26 different letters to fill the first place. We can also use the same number of letters to fill the second place, and the sixth and seventh places too. So there are 2 6 4 possible way to place the letters. We can do the same reasoning for fill the places with the digits. We have 3 places and 10 digits for every place, so there are 1 0 3 way to place digits. So the number of total way we can find to fill the 7 places is 2 6 4 × 1 0 3 = 456976000