A certain office supply store stocks 2 sizes of stick notepads,each in 4 colours : blue,green,yellow or pink.The store packs the note pads in packages that contain either 3 notepads of the same size and the same colour or 3 notepads of the same size and different colours.If the order in which the colours are packed doesnt matter,how many different packages of the types described above are possible?

a)6
b)8
c)16
d)24
e)32

Thanks

There are two different cases to consider:
1) All 3 pads the same color
2) The 3 pads are 3 different colors

Case 1: All 3 pads the same color
Take the task of packaging pads and break it into stages.

Stage 1: Select a size
There are 2 possible sizes, so we can complete stage 1 in 2 ways.

Stage 2: Select 1 color (to be applied to all 3 pads)
There are 4 possible colors from which to choose, so we can complete stage 2 in 4 ways.

By the Fundamental Counting Principle (FCP) we can complete the two stages in (2)(4) ways (= 8 ways)


Case 2: The 3 pads are 3 different colors
Take the task of packaging pads and break it into stages.

Stage 1: Select a size
There are 2 possible sizes, so we can complete stage 1 in 2 ways.

Stage 2: Select 3 different colors
There are 4 possible colors, and we must choose 3 of them.
Since the order of the selected colors does not matter, we can use combinations.
We can select 3 colors from 4 colors in 4C3 ways (4 ways), so we can complete stage 2 in 4 ways.

By the Fundamental Counting Principle (FCP) we can complete the two stages in (2)(4) ways (= 8 ways)


So, both cases can be completed in a total of 8 + 8 ways =[spoiler] 16 = C[/spoiler]

--------------------------

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HI abhasjha,

The question is essentially about the Combination Formula and following instructions. However, if you don't realize that, then you can always "brute force" the solution - you just have to draw it all out.

We're told that there are 2 sizes of notepads and 4 colors (Blue, Green, Yellow, Prink) of notepads. For organizational purposes, I'm going to refer to the 8 types of pads as:

B = Big blue pad
b = Little blue pad
G = Big green pad
g = LIttle green pad
Etc.

Now, we just need to figure out how many options fit each description:

1st: 3 notepads of the SAME SIZE and SAME COLOR....

BBB
bbb
GGG
ggg
YYY
yyy
PPP
ppp

8 options

2nd: 3 notepads of the SAME SIZE and 3 DIFFERENT COLORS

BGY
BGP
BYP
GYP
bgy
bgp
byp
gyp

8 options

Total options = 8 + 8 = 16

Final Answer: C

GMAT assassins aren't born, they're made,
Rich