Problem Solving

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.

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.

Thank you so much. I was multiplying the result of I & II. Now i understand it.

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.