Question 1088487
Question:
A design of face is to be painted using a different color for the face, the eyes (both of which have to be the same color), the nose and the mouth. If 6 different colors are available, how many designs are possible? 
 
Solution:
First choose 4 colours out of the 6 in C(6,4)=15 ways.
Then the 4 colours can be applied to the four locations in 4!=24 ways.
The total number of different faces is therefore 15*24=360.