Erial numbers for a product are to be made using 4 letters followed by 3 digits. the letters are to be taken from the first 9 letters of the alphabet, with no repeats. the digits are taken from the 10 digits 0, 1, 2, ..., 9, with no repeats. how many serial numbers can be generated?

Question

Melissa Kline

Mathematics

1 May, 05:20

Erial numbers for a product are to be made using 4 letters followed by 3 digits. the letters are to be taken from the first 9 letters of the alphabet, with no repeats. the digits are taken from the 10 digits 0, 1, 2, ..., 9, with no repeats. how many serial numbers can be generated?

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Alexis Morgan · Answer 1

2177280 serial numbers can be formed.

For the first part, we can have

9 (8) (7) (6) = 3024 possibilities. This is because there are no repeats; we can have 9 for the first letter, 8 for the second, and so on.

For the numeric part, we can have

10 (9) (8) = 720 possibilities. This is because there are no repeats; we can have 10 for the first number, 9 for the second, and so on.

Together, this gives us 3024 (720) = 2177280.