A new flag is to be designed with six vertical stripes using some or all of the colours yellow, green, blue and red. Then, the number of ways this can be done such that no two adjacent stripes have the same colour is:
Explanation:
The first stripe can be coloured in 4 ways. Then the second can be coloured in 3 ways. The third, fourth, fifth and sixth can be coloured thereafter in 3 ways each.
∴ The total number of ways in which the flag can be coloured
= 4 × 3 × 3 × 3 × 3 × 3
= 12 × 81 ways.
Hence, option (a).
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