# A Potential Exam Question: Junior Cert

One of the many unique questions we cover in our annual blitz! This is aimed at **Junior Certificate Higher Level**. For a Leaving Cert question, go here.

### Can you answer this question on arrangements?

- A password consists of one digit from 1 to 9 followed by one of the letters V, W, X, Y or Z. How many different passwords are possible?
- Another password consists of one digit from 1 to 9 followed by a letter. How many different letters are required to allow a total of 72 different passwords?

### Don't open the solution till you've tried it yourself!

## Our Solution

- There are 9 possible values for the first character and 5 different letters for the second character, so a total of 9 × 5 = 45 possible passwords.
- Let's assume we have
*x*different letters. We still have 9 possible values for the first character, so in total we have 9*x*passwords. This gives 9*x*= 72. We can divide both sides by 9 to get*x*= 8. That is, we require 8 different letters in order to have 72 different passwords.

For more questions like this, sign up for our maths blitz for the best preperation for your Junior Cert Higher Level exam, held a few days before each paper.