# help with factorials

• Oct 10th 2007, 03:52 PM
simone
help with factorials
A certain office supply store stocks 2 sizes of self-stick notepads, each in 4 colors. The store packs the notepads in packages that contain either 3 notepads of the same size and color or 3 notepads of the same size and of 3 different colors. If the order in which the colors are packed is not considered, how many different packages of the types described above are possible?
• Oct 10th 2007, 07:27 PM
Soroban
Hello, Simone!

Quote:

A certain office supply store stocks 2 sizes of self-stick notepads, each in 4 colors.
The store packs the notepads in packages that contain
either 3 notepads of the same size and color
or 3 notepads of the same size and of 3 different colors.
If the order in which the colors are packed is not considered,
how many different packages of the types described above are possible?

For a type-A package (two sizes, one color), there are:
. . 2 choices of sizes and 4 choices of colors.
There are: $\displaystyle 2\cdot4 \:=\:8$ possible type-A packages.

For a type-B package (two sizes, three colors), there are:
. . 2 choices of sizes and $\displaystyle {4\choose3} = 4$ choices of colors.
There are: .$\displaystyle 2\cdot4\:=\:8$ possible type-B packages.

Therefore, there are: .$\displaystyle 8+8\:=\:16$ possible packages.