Serial numbers for a product are to be made using 2

 letters followed by 2

 digits. The letters are to be taken from the first 8

 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?

The number of serial numbers that can be generated is 5040.

Step-by-step explanation

Serial numbers for a product are to be made using 2  letters followed by 2 digits.

The letters are to be taken from the first 8 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?

The letters are to be taken from the first 8 letters of the alphabet, with no repeats.

For the first letter, there are 8 letters of choice.

For the second letter since repetition is not allowed and one letter is used during the first selection, there are only 7 letters of choices left.

The number of ways to select 2 letters from the first 8 letters of the alphabet, with no repeats.

8P2 = 8 x 7 = 56

The digits are taken from the 10 digits 0,1,2,...,9, with no repeats.

For the first digit, there are 10 digits of choice.

For the second digit since repetition is not allowed and one digit is used during the first selection, there are only 9 digits of choices left.

The number of ways to select 2 digits from the first 10 digits, with no repeats.

10P2 = 10 X 9 = 90

The number of serial numbers that can be generated is

56 x 90 = 5040