A flag has to be designed with 4 horizontal strips using some or all of the colour 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?

Correct Option (C)

The design of a flag with four horizontal strips, where no two adjacent strips share the same colour, can be determined by considering the choices for each strip sequentially:

• For the first strip, there are 3 available colour choices (red, green, yellow).
• For the second strip, as it must differ from the first, there are 2 remaining colour choices.
• For the third strip, as it must differ from the second, there are 2 remaining colour choices.
• For the fourth strip, as it must differ from the third, there are 2 remaining colour choices.

Therefore, the total number of different ways to design the flag is calculated as \( 3 \times 2 \times 2 \times 2 = 24 \) ways.

Incorrect Options:

Options (A) 12, (B) 18, and (D) 36 are incorrect. These values do not align with the correct application of the permutation principle under the given constraints. Incorrect results could arise from errors in calculating the number of available choices for each strip or from miscalculations in the final product. The correct methodology requires multiplying the number of valid choices for each strip, ensuring the adjacency rule is consistently applied.