A flag has to be designed with 4 horizontal stripes using some or all of the colours red, green and yellow.…
A flag has to be designed with 4 horizontal stripes using some or all of the colours red, green and yellow. What is the number of different ways in which this can be done so that no two adjacent stripes have the same colour?
12
18
24
36
Solution
The first stripe can be any of 3 colours. Each subsequent stripe must differ from the one above it, giving 2 choices each. Total $= 3 \times 2 \times 2 \times 2 = 24$.