Question 1133886: In a certain region all license plates are composed of three letters followed by three numbers, or three numbers followed by three letters. The only restriction is that zero can never be the first of the three numbers if the three numbers come first. Find how many license plates are possible.
Found 2 solutions by Glaviolette, math_tutor2020:
Answer by Glaviolette(140)   (Show Source):
You can put this solution on YOUR website! The first space can either be a number (other than 0) or a letter, therefore, there are 35 options (26 + 9). If the first space is filled with a number, there are then 10 options for the second space and 10 for the third space (keeping them numbers). The last 3 spaces would be letters, 26 options for each. Using the counting principle, these values are multiplied...
35*10*10*26*26*26 = 61516000
If the first space was filled with a letter, there are 26 options for space 2, 26 for space three. Then switching to numbers, 10 options for each of the remaining 3 spaces.
35*26*26*10*10*10 = 23660000
For a total of 85176000 possible license plates. Wow, that was fun!
Answer by math_tutor2020(3817)  (Show Source):
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