msand 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
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 colorTake 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 colorsTake 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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