Probability

[moneyman]

A certain office suppl store stocks 2 sizes of notepads, each in four colors: blue,yellow,green 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??

6
8
16
24
32

Ans C

[VP_RedSoxFan]

When you post you can help out by also giving the answer. That way, I know I'm actually helping!

First I'll consider the number of packs of same size, same color. There are 4 colors and 2 sizes, so that is (4 * 2) = 8 total different packages of same size and color.

Now we'll consider the other type, same size, 3 different colors. If we just consider one size, the big notebooks first, then we can get the number of different combinations of big notebooks/different colors by the combinations (since order doesn't matter) formula 4_C_3 = 4!/(3!(4-3!)) = 4. That tells us that there are 4 different combinations of packs of 3 colors.

Since we can have those same 4 combinations of colors in small notebooks, the answer is then:

8 same size/color + 4 big/different colors + 4 small/different colors = 16 total combinations.

Hope this helps, good luck!

[moneyman]

Hi Ryan,
I have given the answer whose font color is in white. I do this so that people dont get distracted when they work out the problem.

[moneyman]

I am sorry but I really dint get a hang of the explanation. Maybe because I really suck at probability questions. Can you pls expalin further??