Question

In Nova Scotia we use a distinctive combination of letters and numbers to represent the license plates we display on our vehicles. The pattern used is 3 letters followed by 3 numbers. If the number zero is not permitted and the other letters and numbers may be repeated how many possible license plates could be issues without a repeat pattern?

Answer 1

There are 26 alphabets (A-Z) and 10 numbers (0-9), since we are not permitted to have number zero, we are left with 26 alphabets and 9 numbers (1-9)

We need to fill it without repeating, the first alphabet can be picked in 26 ways (any of A-Z)

Second one can be picked in 25 ways (anyone except the first alphabet)

Third one can be picked in 24 ways (anyone except the first and second alphabet)

Similarly first number in 9-ways, second number in 8-way and third number in 7 ways

Total ways = 26 * 25 * 24 * 9 * 8 * 7 = 7862400 ways

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