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Q66·CSAT · Prelims 2023

Flag designs with adjacent color constraints

NumericalPermutations & CombinationsNumber theory● Medium

Question

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?

Options

a

12

b

18

c

24

d

36

Answer

Explanation

Calculate the color choices available for each stripe sequentially from top to bottom:

Stripe 1 (Top): Can be filled with any of the 3 available colors (Red, Green, Yellow). Choices = 3.
Stripe 2: Cannot match the color of Stripe 1, leaving exactly 3 - 1 = 2 choices.
Stripe 3: Cannot match the color of Stripe 2. It can, however, reuse the color of Stripe 1. Choices = 2.
Stripe 4 (Bottom): Cannot match the color of Stripe 3, leaving exactly 2 choices.

Multiply the independent choice possibilities together: Total ways = 3 × 2 × 2 × 2 = 24.

For sequential adjacent-color restrictions on N slots using C colors, the total arrangement count is always C × (C-1)^N-1.

Answer: (c).

Question details

Year

2023

Paper

CSAT

Question

Q66

Section

Numerical Ability

Sub-topic

Permutations & Combinations

Type

Number theory

Difficulty

Medium

Source hint

Number theory

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