Exam-Style Question on Combinations
A mathematics exam-style question with a worked solution that can be revealed gradually
Question id: 501. This question is similar to one that appeared on a GCSE Higher paper in 2019. The use of a calculator is not allowed.
There are four dials on a combination lock.
Each dial can be set to one of the numbers 1, 2, 3, 4.
The four digit number 4234 is one way the dials can be set, as shown in the diagram.
(a) Work out the number of different four digit numbers that can be set for the combination lock.
(b) How many of the possible four digit numbers have four different digits?
The worked solutions to these exam-style questions are only available to those who have a Transum Subscription.
Subscribers can drag down the panel to reveal the solution line by line. This is a very helpful strategy for the student who does not know how to do the question but given a clue, a peep at the beginnings of a method, they may be able to make progress themselves.
This could be a great resource for a teacher using a projector or for a parent helping their child work through the solution to this question. The worked solutions also contain screen shots (where needed) of the step by step calculator procedures.
A subscription also opens up the answers to all of the other online exercises, puzzles and lesson starters on Transum Mathematics and provides an ad-free browsing experience.
Drag this panel down to reveal the solution
If you need more practice try the self-checking interactive exercises called Systematic Listing.
©1997 - 2021 Transum Mathematics :: For more exam-style questions and worked solutions go to Transum.org/Maths/Exam/