Question

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 1

Answer:  (C) 16

Step-by-step explanation:

Given : Number of sizes of self-stick notepads= 2

Number of colors = 4

Type 1 : The store packs the notepads in packages that contain 3 notepads of the same size.

i.e. By Fundamental principle of counting , we have

Number of different packages possible = Number of colors x No. of sizes

= $4\times2=8$

Type 2: Notepads of the same size and of 3 different colors.

Choices for 3 different colors out of 4 : $^4C_3=\dfrac{4!}{3!(4-3)!}=4$

Again by fundamental principle :

Number of different packages possible = No. of choices for choosing 3 different colors x No. of sizes

= $4\times2=8$

From Type 1 and Type 2 , the total number of different packages of the types described above are possible =8+8= 16

Hence, the correct answer is option (c) 16.