Answer:
a: 175,760,000
b: 24,240,000
Step-by-step explanation:
For each letter assigned, there can be 10,000 numbers after it (the numbers 0000 through 9999).
There are 26 letters, so when we use all the letters we have assigned
26*10,000 = 260,000 license plates.
Each time we add a letter, we have assigned 26 more options
(AA, AB, ... AZ, BA, BB, ...BZ)
So when we get through 2 letters we have
26*260,000 = 6,760,000 plates
When we add a third letter, we have 26 new cycles of the previous situation.
So we have 26*6,760,000 = 175,760,000 plates
If the district has 200,000,000 cars, then they need
200,000,000 - 175,760,000 = 24,240,000 cars with 4 letters on their plates
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