Question

A new flag is to be designed with six vertical strips 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 strips have the same colour is

• A. $12\times 81$
• B. $16\times 192$
• C. $20\times 125$
• D. $24\times 216$

Answer 1

Answer: (A)

$12\times 81$

First strip can be colored by $=4ways$

2nd strip can be colored by $=3ways$

3rd strip can be colored by $=3ways$

4th strip can be colored by $=3ways$

5th strip can be colored by $=3ways$

6th strip can be colored by $=3ways$

Then total ways$=4\times 3\times 3\times 3\times 3\times 3=12\times 3^4=12\times 81$ Ans.

Hence, this is the answer.

Option (A) is correct answer.