Question

a new flag is to be designed with six verticle stripes using some of all the colors yellow,green , blue and red,then the number of ways this can be done such that no two adjacent stripes have the same color is
a.12* 81
b.16*192
c.20*125
d.24*216

Answer 1

For the first stripe, you have 4 choices. For the second, you have 3 choices, since the previous color cannot be picked. For the third, again you have 3 choices, since it cannot have the same color as the second stripe, but it can take on the color of the first. The remaining stripes likewise have only 3 choices.

Answer 2

so u mean
\(\large\tt \begin{align} \color{black}{4\times3\times 3\times 3\times 3\times 3\\
=4\times 3^5\\
=12\times 81 }\end{align}\)

can u confirm this ?

Answer 3

That's right. Not sure why the possible choices are listed like that.

Answer 4

Ah ok thanks , this for tough entrance exam so they might confuse students