Difficulty: Rating: GCSE Marks:

GCSE Text:
All aircraft in the UK have a unique registration code painted on the side. The code has 5 letters of the alphabet, each A-Z. For the UK, the first letter must be a ‘G’ followed by a dash and then four more A-Z letters that can repeat.

example: A helicopter has the registration of G – HPDG

a) How many unique codes exist for UK aircraft?

For ‘lighter than air’ aircraft (hot air balloons and airships), there are extra rules. In addition to starting with a ‘G’ and dash, the second letter must be an ‘F’ and this time the letters must not repeat.

example: A hot air balloon has the registration of G – FBES

b) How many unique codes exist for ‘lighter than air’ aircraft in the UK?

Suggestions:
This is a good consolidation question for students who have learned listing strategies and probability outcomes and they will need to consider the repeating or non-repeating nature of the codes. Some students like to sketch a probability tree diagram whilst other just remember the rule of multiplication. students as the method is not specified in the question. Students need to select the appropriate trigonometric approach to take as well as consider different units. The extension task works well for higher paper GCSE students too.

Teachers could extend the learning by considering:

• Because aircraft codes are never reused, even for retired or scrapped aircraft, available UK codes are running out as new aircraft are being made. A suggestion is to add an extra letter on the end in future. How many more codes would a 6 letter pattern create compared to the existing 5 letter pattern?