Week 340 (12th April 2024)

Eve is trying to catch up with her homework before she goes back to school next week. 

Eve has been set some maths homework and has one question left….  

How many different 7-digit even whole numbers can be made using the following digits:  

 3, 4, 5, 6, 7, 8 and 9   

Each digit can only be used once.   

Help Eve to finish her homework. 


To make an even number the last digit can only be: 

4, 6 or 8 (so 3 combinations) 

The other six digits can be any combination of the remaining numbers ie 6 factorial. 

6 x 5 x 4 x 3 x 2 x 1 x 3 = 2,160 

Special recognition to Mark Eade who provided an even better explanation as shown below: 

In order to be an even number, the combination would have to end with a 4, 6, or 8. 

So, we can instead look at how many different 6 digit numbers we can make with 3, 5, 6, 7, 8, 9 (where 4 will be at the end) – and then the total number of 7 digit combinations should be three times the [6 digit plus one even number at the end] combinations. 

Number of 6 digit combinations from a selection of 6 different numbers is 6!, or 6x5x4x3x2x1 = 720 

So each 6 digit combination with a 4, 6 or 8 at the end would each have 720 combinations – so total number of even numbers with that selection of numbers is 720×3 = 2,160.