Serial numbers for a product are to be made using 4 letters followed by 2 digits. The letters are to be taken from the first 6 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

Jayden Glover

Mathematics

24 January, 15:01

Serial numbers for a product are to be made using 4 letters followed by 2 digits. The letters are to be taken from the first 6 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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Answers (1)

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Jayson Fry · Answer 1

675

Step-by-step explanation:

This is going to be really hard for you to understand unless you know factorials.

The first four letters is a combination out of 6 letters; we call it 6 choose 4. As you may know, factorial is the multiplication of a number and it's previous digits. For example, 3! = 1 x 2 x 3

The 6 choose 4 is (6!/4!2!) = (5x6) / 2 = 15

The 10 choose 2 is (10!/2!8!) = (9x10) / 2 = 45

Then you multiply both as they're independent:

15 x 45 = 675 serial numbers