Selection of at least two colours Let there be three sketch pens of different colours. A regular pentagon is to be drawn using these colours where exactly one of the colours is used to draw a side and at least two colours are used to make the complete pentagon. In how many ways can this be done?
My attempt:
Each side can be drawn by using any of the three colours , so $3$ choices are available for each side. There are $5$ sides in total so they can be drawn in $3^{5}$ ways and the number of ways in which we can use only one colour is $3$ so the required number of ways $= 3^5 - 3$.
Did i miss anything?
Yes! A pentagon has 5 sides.  You say "they can be drawn in $3^5$ ways" and then include another way to color some, apparently, sixth way side!  What I would do is argue that there are $3^5$ ways to color the five sides but three of those ways include all five sides the same so there are $3^56- 3= 3(3^4-1)= 3(80)= 240 ways to do this.
since it is regular pentagon so anticlockwise and clockwise direction would be same so divide your answer by $5$ that is number of sides.