Exam-Style Question on Combinations

A mathematics exam-style question with a worked solution that can be revealed gradually

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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?

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