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by ruchisharma » Sun Nov 21, 2010 10:46 am
A certain office stores 2 sizes of notepads, each in 4 colours: blue, yellow, green, pink. The store packs notebooks in packages that contain either 3 notepads of same size and same color or 3 notepads of same size and different colors.
If the order in which colors are packed is not considered, how many different packages of the types described above are possible?

6
8
16
24
32
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Source: — Data Sufficiency |
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by shovan85 » Mon Nov 22, 2010 2:43 am
ruchisharma wrote:A certain office stores 2 sizes of notepads, each in 4 colours: blue, yellow, green, pink. The store packs notebooks in packages that contain either 3 notepads of same size and same color or 3 notepads of same size and different colors.
If the order in which colors are packed is not considered, how many different packages of the types described above are possible?

6
8
16
24
32
Type 1: 3 notepads of same size and same color.

2 sort of sizes and 4 sort of colors. So total number of possible packages = 2 * 4 = 8

Type 2: 3 notepads of same size and different colors.

4 different colors. We need to selcet 3 out of them. This can be done in C(4,3) = 4 ways
Total 2 types of sizes.
So total number of possible packages = 2 * 4 = 8

Thus, in total = 8 + 8 =16
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