EXAMPLE 1.5.20

Euclid's Auto Body Shoppe is trying to unload some unwanted paint by offering the following special deal: for $99 you get a two-tone paint job, using one color for the top and a different color for the body. The available colors are: hot pink, puke green, Gator orange, flaming chartreuse. How many different paint schemes are possible?

A. 8 B. 16 C. 12 D. 7

SOLUTION

We need to choose two different colors from a set of four colors. This is a permutation problem, not a combination problem, because (for instance) a car with a hot pink top and a puke green body is different from a car with a puke green top and a hot pink body.

P(4,2) = 12