GMATPrep-Permutation & Combination

prachich1987 wrote:2 sizes of sticky pads. Each has 4 colors – Blue, Green, Yellow, and Purple. The pads are packed in packages that contain either 3 notepads of same size and same color or 3 notepads of same size and of 3 different colors. How many different packages of the types described are possible?

a. 6
b. 8
c. 16
d. 24
e. 32

you definitely have to enumerate the two different kinds of packages (one type with three of the same color, the other type with three of different colors) separately.

for the type with 3 of the same color:
since everything is one color, the number of differently colored packs is the same as the number of colors, i.e., 4.
so that's four different packs of each size; since there are two sizes, that's a total of 8 packs of this type.

for the type with 3 of different colors:
the number of different selections of colors is 4c3 = 4 (or just count them: BGY, BGP, BYP, GYP, or "everything but blue", "everything but yellow", "everything but green", "everything but purple").
again, four different packs of each size; since there are two sizes, that's a total of 8 packs of this type.

total 16 packs.