Answered

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.

Answer :

whitneytr12

Answer:

Option C. 16

Step-by-step explanation:

Number of differents colors = 4

Number of differents sizes = 2

Case 1: 3 notepads of the same size and the same color:

If we have a package with the same size and the same color, the number of possible packages is:

N° packages = 4(colors)*2(sizes) = 8

Case 2: 3 notepads of the same size and different colors:      

In this case, to calculate the number of possible permutations of packages without repetitions we need to use the following equation:    

[tex] C_{n}^[p} = \frac{n!}{p!(n-p)!} [/tex]

where p: is the number of colors for each package = 3, and n: is the total number of colors = 4.

[tex] C_{4}^[3} = \frac{4!}{3!(4-3)!} = \frac{4*3*2*1}{3*2*1} = 4 [/tex]

This number calculated is for one size, if the have two different sizes the number of possible packages is:

N° packages = 4(colors)*2(sizes) = 8    

Therefore, the total number of different possible packages is:

N° packages = case 1 + case 2 = 8 + 8 = 16

So, the correct answer is option C = 16.

I hope it helps you!

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