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Need help with PS question

by harmeet » Mon Jun 14, 2010 9:59 pm
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

Can you please show how me with this problem?

Thanks,
Harmeet.
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by Testluv » Mon Jun 14, 2010 11:36 pm
There are two sizes of notepads and four different colors for each notepad.

The store sells two categories of notepads:

I same size and same color
II same size and all different colors.

Let's consider I first. There are four different colors. So, we can have all blue or all green etc. But there are two different sizes. So we can have all small/blue or all large/blue or all small/green or all large green etc. So, in I, there are 4*2 or 8 different types of notepads.

For II, we have four colors from which we are selecting any three. So, there are 4C3 = 4C1 = 4 ways we can have three different colors. Again, there are two different sizes, so here we also have 4*2 = 8 different types of notepads.

So, all told there are 8 + 8 = 16 types of notepads.
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by harmeet » Tue Jun 15, 2010 12:03 am
Thank you so much. I was multiplying the result of I & II. Now i understand it.
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by Testluv » Tue Jun 15, 2010 12:06 am
harmeet wrote:Thank you so much. I was multiplying the result of I & II. Now i understand it.
No worries. In combinatorics/probability, when you have "or" you add and when you have "and" you multiply. Here, we can have a notepad package in I OR a notepad package in II.
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