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
Thanks
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Number of notepads of the same color = 4 (blue, green, yellow, pink)alex.gellatly 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
Thanks
Since there are two different sizes, so total number of notepads for the same color = 4 * 2 = 8
We have to choose 3 different colors from 4, so notepads of different colors = 4C3 = 4
Since there are two different sizes, so total number for the different color = 4 * 2 = 8
Therefore, required number of packages = 8 + 8 = 16
The correct answer is C.
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Since there is too much information in the question, we can start by making a few symbols to get a better clarity into the question as follows:
Let B, G, Y, P be the big-sized notepads.
Let b, g, y, p be the small-sized notepads.
For Three notepads of same size and same colour we can have a package containing 3 of each of B, G, Y, P, b, g, y and p. such as (B,B,B), (y,y,y), etc. That's a total of 8 packages.
+
For 3 notepads of the same size and of 3 different colors, you can selected three from the big-sized one or 3 from the small-sized ones = 4C3 + 4C3 = 8
8 + 8 = 16
(C) is the answer.
Let B, G, Y, P be the big-sized notepads.
Let b, g, y, p be the small-sized notepads.
For Three notepads of same size and same colour we can have a package containing 3 of each of B, G, Y, P, b, g, y and p. such as (B,B,B), (y,y,y), etc. That's a total of 8 packages.
+
For 3 notepads of the same size and of 3 different colors, you can selected three from the big-sized one or 3 from the small-sized ones = 4C3 + 4C3 = 8
8 + 8 = 16
(C) is the answer.
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2C1*4C1+4C3*2C1 = 8 + 8 = 16
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i understand till here, why did we do after that 8 +8?[/quote]Number of notepads of the same color = 4 (blue, green, yellow, pink)
Since there are two different sizes, so total number of notepads for the same color = 4 * 2 = 8
We have to choose 3 different colors from 4, so notepads of different colors = 4C3 = 4
Since there are two different sizes, so total number for the different color = 4 * 2 = 8
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Because the question said "... 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"amyhussein wrote:i understand till here, why did we do after that 8 +8?
Those are two different scenarios.
For each of them, 8 different packages are possible.
Hence, total number of possible packages = (8 + 8) = 16
Hope that helps.
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I am a bit confused,
How. An we choose 3 packs with same size and colour if already each size contains total of 4 notes each in different colors. My understanding is that there are no multiple notes with same colour within the same size. What am I missing here
How. An we choose 3 packs with same size and colour if already each size contains total of 4 notes each in different colors. My understanding is that there are no multiple notes with same colour within the same size. What am I missing here
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The problem said only the following things,amyhussein wrote:I am a bit confused,
How. An we choose 3 packs with same size and colour if already each size contains total of 4 notes each in different colors. My understanding is that there are no multiple notes with same colour within the same size. What am I missing here
- There are notepads of two different size, say large and small.
Each size has four different colors: blue, green, yellow, or pink.
In fact, there are multiple number of notepads of same color and same size. Otherwise how the store will pack the notepads in packages that contain 3 notepads of the same size and the same color?
Your mistake is you are assuming that "each size contains total of 4 notes each in different colors"
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There are two different cases to consider:alex.gellatly wrote: ↑Tue Apr 17, 2012 4:55 amA 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
Thanks
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