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

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*2=8`

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

Choices for 3 different colors out of 4 :
`^4C_3=(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*2=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.