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Question
In how many ways can this diagram be coloured subject to the following two conditions?
(i) Each of the smaller triangle is to be painted with one of three colours: red, blue or green.
(ii) No two adjacent regions have the same colour.
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Solution
These conditions are satisfied exactly when we do as follows:
First paint the central triangle in any one of the three colours.
Next paint the remaining 3 triangles, with any one of the remaining two colours.
By the fundamental principle of counting
This can be done in 3 × 2 × 2 × 2 = 24 ways.
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