Sticky Pads

[okigbo]

2 sizes of sticky pads. Each has 4 colors - Blue, Green, Yellow, and Purple. The pads are packed in packages that contain either 3 notepads of same size and same color or 3 notepads of same size and of 3 different colors. How many different packages of the types described are possible?
a. 6
b. 8
c. 16
d. 24
e. 32

[NikolayZ]

Hey!

You got 2 sizes of pads.
and 4 different colors.

Let's count all possible different packages.

1) Same size , same color.
Only 4. But we have 2 sizes, then 8 packages of this type.
2) Same size, different color.
We have to choose from 4 colors. Order doesn't matter.
4!/3!=4. Also, we need to multiply this one by 2, because we have 2 sizes. so, 8.
Overall, 8+8=16 different packages.
Hope it is clear.
P.s. I remember that this problem was solved here couple of days ago. You can search for it. Afaik, there was a nicer explanation that mine.

[sanjana]

Notepad sizes : S1,S2
Colours : B,G,Y,P
Case 1 : Same size and same coulour
Number of ways of picking 3 notepads of the same size

First Notepad : 2 ways
Based on the size of the 1st notepad there will be only 1 way to pick the 2nd and 3rd
2 * 1* 1
Same colour : picking 1 colour out of 4 : 4c1 = 4 ways

Total ways : 2*4 = 8

Case 2 : same size and diff coulour

Same size : 2 ways
Different colour

B G Y P
Y Y Y N

No of ways : 4!/3!*1! = 4
Total ways of case 2 = 4*2 = 8

Required answer : 8+8 =16