A flag has to be designed with 4 horizontal strips 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?

1. A. 12
2. B. 18
3. C. 24
4. D. 36

Answer: C

Explanation

We need to design a flag with 4 horizontal stripes using three colors (red, green, yellow), such that no two adjacent stripes have the same color. Let’s determine the number of choices for each stripe:
1. For the first stripe: There are 3 available colors (Red, Green, Yellow). So, 3 choices.
2. For the second stripe: It must be different from the first stripe. This leaves 2 choices.
3. For the third stripe: It must be different from the second stripe. This again leaves 2 choices (it can be the same color as the first stripe, but not the second).
4. For the fourth stripe: It must be different from the third stripe. This also leaves 2 choices.
To find the total number of different ways, we multiply the number of choices for each stripe: 3 × 2 × 2 × 2 = 24 ways. This question tests basic principles of permutations and combinations with restrictions, a common topic in CSAT.