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Joined: 20 Feb 2017
Posts: 2506
Given Kudos: 1053
GPA: 3.39
A certain office supply store stocks 2 sizes of self-stick notepads, e
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16 Apr 2022, 04:17
16 Apr 2022, 04:17
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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
A. 6
B. 8
C. 16
D. 24
E. 32
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Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: A certain office supply store stocks 2 sizes of self-stick notepads, e
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16 Apr 2022, 05:57
16 Apr 2022, 05:57
3
GeminiHeat 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
A. 6
B. 8
C. 16
D. 24
E. 32
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 GRE. So, be sure to learn it.
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Re: A certain office supply store stocks 2 sizes of self-stick notepads, e
[#permalink]
16 Apr 2022, 06:56
16 Apr 2022, 06:56
1
Quote:
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?
There are two possible cases:
Case 1: packages that contain 3 notepads of the same size and the same color
In one size, there are 4 choices of same colour
In other size, there are 4 choices of same colour
Total ways of packages that contain 3 notepads of the same size and the same color = 4 + 4 = 8
Case 2: packages that contain 3 notepads of the same size and of 3 different colors
In one size, 3 different colors can be packed in 4C3 ways = 4, as the order does not matter
In other size, 3 different colors can be packed in 4C3 ways = 4
Total ways of packages that contain 3 notepads of the same size and of 3 different colors = 4 + 4 = 8
Total number of ways 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) = 8 + 8 = 16 ways
IMO C
