Question

A new flag is to be designed with six vertical strips using some or all of the colour 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

The correct option is A $12\times 81$

From the condition for $1^{st}$ strip we have $th$ color option and $2^{nd},3^{rd},4^{th},5^{th},6^{th}$ we have $3$ colours for each became the previous color cannot be used

$=4\times 3^5$

$12\times 8^1$