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 2 size options: small and large.
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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