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License plates for cars have to be unique. If a license plate contains 6 characters consisting of 2 letters followed by 4 digits example: QW2354,
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| Solve | Step |
| How many different license are possible? | |
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There are 26 × 26 × 10 ×
10 × 10 × 10 |
Multiplication
Principle 26 letters, 10 digits 0 - 9 |
| Letters repeated but not numbers... | |
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26 × 26 |
Start with 26 letters . Repeats allowed such as AA or BB etc... |
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26 × 26 × 10 × 9 × 8 × 7 = |
Repeating
numbers are not allowed. 1174, 1231, 1111 are not allowed. |
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If the first 3 characters are AA4, then the next number can't be 4. There are only 9 numbers left to choose from. If the next number is 2, AA42, there are only 8 numbers left to choose from and so on.... |
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There are 26 × 26 × 10 × 9 × 8 × 7 = 3,407,040 different plates with no repeating numbers. |
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