Question

The Joe Llama library is redoing their inventory system. Books will be given unique codes that consist of 4 upper case letters from A to Z followed by a numbers from 0 to 9. What is the
maximum number of books that the library could assign codes to using this system?

PLEASE HELP

Answer 1

Each book must have a unique code, then we want to find the total number of combinations of 4 upper cases followed by a number.

We will see that the maximum number of books that the library could assign codes using this system is 4,569,760

To find the total number of combinations, first, we need to find each selection.

Here we have 5 selections:

• first letter:
• second letter:
• third letter:
• fourth letter:
• number:

Now we want to find the number of options for each one of these selections.

Assuming that the letters can be used multiple times, for each one of the letters we have 26 options (from A to Z)

And for the number, we have 10 options (for 0 to 9)

Then we have:

• first letter: 26 options
• second letter: 26 options
• third letter: 26 options
• fourth letter: 26 options
• number: 10 options

The total number of combinations is just the product between all of these numbers of options, we will get:

C = 26*26*26*26*10 = 4,569,760

So there are 4,569,760 different codes, thus, the maximum number of books that the library could assign codes using this system is 4,569,760

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