Problem Solving

A certain office supply store stocks 2 sizes of self stick pads, each in 4 colors: blue, green, yellow or pink. The store packs the note pads in packages that contain either 3 note pads of the same size and same color or 3 note pads 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

C 16

3 note pads of the same size and same color
First you can make 8 package of the same size and same color; one small and one big for each of the 4 colors so 8

3 note pads of the same size and of 3 different colors
For small size you can make 4C3 combinations, so 4 possibilities
For big size you can also make 4

So, in total it gives you 16

Can someone explain this in more detail? Tx.

crackgmat007 wrote:Can someone explain this in more detail? Tx.

Lets take a 2 step approach.

A) 3 note pads of the same size and same color.

We have to 2 choices for size and 4 choices for color. -> 2 * 4 = 8

B) 3 note pads of the same size and of 3 different colors

Since we have to choose 3 DIFFERENT colors, we can apply the formula 4choose3 -> 4! / (3! * 1!) = 4.

Now for each of these color combinations we have the option of 2 sizes...hence 4 * 2 = 8.


From A and B, we get 8 + 8 = 16.


** For part B **
It is important to use 4choose2 ...coz if we think of it as 4 choices for each spot then we get 4 * 4 * 4....we would be overcounting in this case as we can get the possibility of 2 pads being the same color (Red, Red, Blue) which cannot be the case.... to eliminate this if we consider 4 choices for the 1 one...and 3 choices for the second one...we wuold use 4 * 3 * 2 as possible solutions but then we are saying that order does matter so (Red, Green, Blue) is different from (Blue, Green Red) or (Green, Red, Blue).

Hope this helps.