Jump to content

How would u solve this problem?

Recommended Posts

Student passwords consist of three letters chosen from A to Z, followed by four digits chosen from 1–9. Repeated characters are allowed. How many possible passwords are there? [4 marks]

Share this post

Link to post
Share on other sites

Representing the three letters with A and the four digits with 1, some of the possible permutations are as follows:

There are 7!/(4!*3!) possible permutations in total.

Each letter has 26 possibilities and each digit has 9 possibilities. (as 0 is not an option)
This gives us 26^3 ways of choosing the three letters and 9^4 ways of choosing the four digits. (Order matters here: AAB ≠ ABA)

Now we simply multiply the three results.
That is,

That easy.

Share this post

Link to post
Share on other sites


I believe letters "followed by" digits means precisely AAA1111, not any of the other options of mixing letters and numbers.

So I think answer was just (26^3)(9^4). Possibly (52^3)(9^4) if including both capitals and lowercase.

Share this post

Link to post
Share on other sites

Create an account or sign in to comment

You need to be a member in order to leave a comment

Create an account

Sign up for a new account in our community. It's easy!

Register a new account

Sign in

Already have an account? Sign in here.

Sign In Now


Important Information

We have placed cookies on your device to help make this website better. You can adjust your cookie settings, otherwise we'll assume you're okay to continue.