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 pacakages 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
How will i find the correct solution to this? Can some experts help?
OA C
A certain office supply store stocks 2
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There are 2 size options: small and large.lheiannie07 wrote: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
There are 4 color options: blue, green, yellow, and pink.
Case 1: 3 notepads of the same size and of the same color
Number of ways to choose 1 size from 2 choices = 2C1 = 2.
Number of ways to choose 1 color from 4 choices = 4C1 = 4.
To combine these options, we multiply:
2*4 = 8.
Case 2: 3 notepads of the same size and of 3 different colors
Number of ways to choose 1 size from 2 choices = 2C1 = 2.
Number of ways to choose 3 colors from 4 choices = 4C3 = (4*3*2)/(3*2*1) = 4.
To combine these options, we multiply:
2*4 = 8.
Total ways to form a package = 8+8 = 16.
The correct answer is C.
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BTGmoderatorDC wrote: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 pacakages 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
How will i find the correct solution to this? Can some experts help?
OA C
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 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: C
GMAT assassins aren't born, they're made,
Rich
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
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There are two different cases to consider:BTGmoderatorDC wrote: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 pacakages 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
How will i find the correct solution to this? Can some experts help?
OA C
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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