A certain office supply store stocks 2 sizes of self-stick notepads

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

Notepads of the same color = 4 (we have 4 colors). As we have two sizes then total for the same color=4*2=8

Notepads of the different colors = 4C3=4 (we should choose 3 different colors out of 4). As we have two sizes then total for the different color=4*2=8

Total=8+8=16

Answer: C.
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Kotela,

Sorry if I was not clear. I generally keep my answers short.

There are two ways this can happen.:

1. Same size same color:
There are eight such combinations
size 1
1-BBB
1-GGG
1-YYY
1-PPP
size 2
2-BBB
2-GGG
2-YYY
2-PPP

total 8

2. Same size different color
size 1
4C3 = 4 (BGY, BYP, GYP, BGP)
size 2
4C3 = 4 (same as above)
Total 8

Notice there there is an OR in the stem, so add
8 + 8 = 16

Hope this helps!

Sure.

As the pads are packed in packages that contain only the notepads of same size then let's calculate for one size and then multiply it by 2 to get total.

There are 4 colors so there are 4 different packages possible with 3 same color notepads: all 3 Blue, all 3 Green, all 3 Yellow, or all 3 Purple;

For 3 different color pads: again as there are 4 colors then 4C3=4 is the # of ways to choose 3 different color pads to make a package: {BGY}, {BGP}, {BYP}, {GYP};

So for one size there are 4+4=8 packages possible thus for 2 sizes there are 8*2=16 packages possible.

Answer: C.

Hope it's clear.
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bunuel can you make me more clear, how it is 4 books of same colour

thank u

First scenario 2C1 * 4C3 = 8
Second scenario 2C1*4C1 = 8

Total 16

Hence, answer is C

Hope it helps
Cheers!
J

Hi All,

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:

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

we have 2 types of notebooks.
we can select either 3 colors or 1 color
to select 3 colors: 4C3 = 4
to select 1 color: 4C1 = 4
so for each type of notebook, we have 8 possible arrangements
8x2 = 16

C

1. Ordering is not important, so this is a combination problem
2. Is there a constraint? There are two cases each with a constraint
3. In the first case ,Constraint is 3 notebooks of the same color . So there are 2 ways of selecting a size and 4C1 ways of selecting a color. So a total of 2*4= 8 ways
4. In the second case, constraint is 3 notebooks of the same size but 3 different colors. There are 2 ways of selecting a size and 4C3 ways of selecting colors, for a total of 2*4=8 ways
5. Total number of combinations is (3) + (4) = 16
_________________

Let’s say the 2 sizes of notepads are small and large. Then, for the small notepads, there are 4 packages of notepads of all the same color (one package for each color) and 4C3 = 4 packages of notepads of three different colors. Thus, for the small notepads, there are a total of 4 + 4 = 8 different packages. Similarly, there are 8 different packages for the large notepads. Thus, there are a total of 8 + 8 = 16 different packages for the 2 sizes of notepads.

Answer: C
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Hi Bunuel,

Sorry but I don't follow this..

When there are 4 colors and 2 sizes there are total of only 8 notepads..how can we have 3 blue. 3 green 3 yellow and 3 purple

Pls explain..what am I missing here?

Thanks In advance

Regards

A certain office supply store stocks 2 sizes of self-stick notepads, each in 4 colors: Blue, Green, Yellow Or Pink. So, we have:

Large size notepads:
4 BLUE
4 GREEN
4 YELLOW
4 PINK

Small size notepads
4 blue
4 green
4 yellow
4 pink
_________________

Hello,

What if there where 5 colours total.

Hi andresan,

Even if there were 5 colors (instead of 4), the approaches would not change - you can either use the Combination formula or 'brute force' the list of options. Have you attempted either approach (and what answer did you get?)?

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

A certain office supply store stocks 2 sizes of self-stick notepads, each in 4 colors: Blue, Green, Yellow Or Pink. So, we have:

Large size notepads:
4 BLUE
4 GREEN
4 YELLOW
4 PINK

Small size notepads
4 blue
4 green
4 yellow
4 pink[/quote]

Shouldn't this be:

For large size..
3 Blue
3 Green
3 Yellow
3 Pink

For small size..
3 Blue
3 Green
3 Yellow
3 Pink

Hi ishaan100,

The numbers "4" and "3" have specific meanings in the context of this question - and do NOT refer to the total number of notepads in the store.

1) There are 4 different colors of pad: Blue, Green, Yellow and Pink - and each color appears in 2 different sizes.
2) Each package contains 3 types of pads: either all the same size & color OR the same size & 3 different colors.

Most of the posts in this thread define how there are 16 POSSIBLE packages of notepads - but again, that has nothing to do with the actual number of notepads in the store.

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

Hi Gmat700Knight, chetan2u

I am just starting on P&C so I too struggle with it. Therefore, I want to ask something about this question. I have gone through all the solutions provided on this thread but I am not being able to clear my head about something. How did we take into account that fact that we have to make 3 notepads.

We have to make either 3 notepads of the same size and the same color or 3 notepads of the same size and of 3 different colors right?
3 notepads of the same size and the same color + 3 notepads of the same size and of 3 different colors right
Choose 1 size out of 2 and Choose 1 color out of 4 + Choose 1 size out of 2 and Choose 1 color out of 4
2C1 * 4C1 + 2C1 * 4C3 = 16
I understood this but how did me make 3 notepads though ?

Thank you,
Dablu

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 = 16

Answer: C

Note: the FCP can be used to solve the MAJORITY of counting questions on the GMAT. So, be sure to learn it.

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Hi Bunuel,

I can't understand this question or any of the solutions one bit, can you please help me..