CAT 2004 — QA Question 32
Answer the following question based on the information given below.
In an examination, there are 100 questions divided into three groups A, B and C such that each group contains at least one question. Each question in group A carries 1 mark, each question in group B carries 2 marks and each question in group C carries 3 marks. It is known that the questions in group A together carry at least 60% of the total marks.
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:
Answer & solution
12 × 81
- B
16 × 192
- C
20 × 125
- D
24 × 216
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).