A transport lorry consists of a cab and a trailer - OCR - GCSE Maths - Question 13 - 2019 - Paper 4

Alfie has 8 colours available for painting.

1. He can choose one colour for the cab, which gives him 8 options.
2. For the trailer, he has to choose a different colour. This means he has 7 remaining options after choosing the cab's colour.
3. For his name on the trailer, he again needs to select a different colour from both the cab and the trailer, leaving him with 6 options.

Thus, the total number of ways Alfie can paint his model lorry can be calculated as:

$$8 imes 7 imes 6 = 336.$$

Alfie can paint his lorry in 336 different ways.