SOLUTION: 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 availa

Question 1088487: 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?
a. 120
b. 240
c. 360
d. 720
Found 2 solutions by mathmate, KMST:
Answer by mathmate(429) (Show Source): You can put this solution on YOUR website!
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.
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
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 choices of colors.
When you want to paint a second feature, you have colors to chose from.
When you want to paint a third feature, you have colors to chose from.
When you want to paint the fourth and final feature, you have colors to chose from.
choices multiply, so the total number of designs is
.
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