and we have a winner!!!

We have 3 colors and 5 panels.

Step 1

Total combinations therefore are 3^5=243

Step 2

We now need to remove all the combinations where only 2 or less are used.

2^5=32 We have 3 combinations of paint Red/Blue Red Green Blue/Green

(2^5)*3=96

243-96=147

Step 3

We now have 147 however in step two we removed all red/blue/green combinations twice. i.e. once for Red/Blue and once for Red/Green which would remove RRRRR twice.

We add this 3 back to arrive at 150

Answer = 150