Question 1088487
ANOTHER WAY:
If you are going to do the painting, you have some freedom. It does not matter what feature you paint first. All possible designs you could get are the same designs, if you start with the eyes, or with the mouth, or ...
For the first feature you choose to paint, you have {{{6}}} choices of colors.
When you want to paint a second feature, you have {{{6-1=5}}} colors to chose from.
When you want to paint a third feature, you have {{{6-2=4}}} colors to chose from.
When you want to paint the fourth and final feature, you have {{{6-3=3}}} colors to chose from.
choices multiply, so the total number of designs is
{{{6*5*4*3=360}}} .