soni_pallavi wrote: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.
Aside: If anyone is interested, we have a free video on calculating combinations (like 4C3) in your head:
https://www.gmatprepnow.com/module/gmat-counting?id=789
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]
Cheers,
Brent
Aside: For more information about the FCP, we have a free video on the subject:
https://www.gmatprepnow.com/module/gmat-counting?id=775
