The answer is (c) 16.
First we need to determine the number of ways we can pull 3 different colors from 4. This would be combinatorics (spelling?)
\(C_3^4 = \frac{4!}{3!1!} = 4\)
4! = 24 3! = 6 and 1! = 1. so 24 / 6 = 4. (This could also be seen as selecting 1 from 4, with that 1 being the color NOT in the package, because when you select 1, you leave 3 in a group as well. Same cat, different way to skin it.)
Now we have to take into account the different sizes (2 sizes) and the ways to package (all same color or different colors.)
If pacakged all with the same color, then there are 4 ways to package the notepads because there are 4 colors. So for each method of colors, either different or the same, there are 2 sizes, so 4 x 2 = 8. Now for the ones that are packaged with different colors, there are 4 combinations and 2 sizes, so 4 x 2 = 8. 8 + 8 = 16.
Now that you see the basis for this, look at it this way.
Number of ways to package based upon color * number of sizes = Total combinations.
Ways to package 3 different colors = 4 and 4 ways if all same color, so a total of 8 possibilities. 2 sizes = 8 x 2 = 16.
jallenmorris wrote:
A certain office supply store stocks 2 sizes of self-stick notepads, each in 4 colors: blue, green, yellow, or pink. The store packs the notepads in packages that contain either 3 notepads of the same size and the same 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?
(a) 6
(b) 8
(c) 16
(d) 24
(e) 32
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J Allen Morris
**I'm pretty sure I'm right, but then again, I'm just a guy with his head up his a$$.
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