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

The answer is C. 16

Explanation:

Notepads of the same color = 4

As we have two sizes then total for the same color =
`4*2=8`

Notepads of the different colors as we have to choose 3 different colors out of 4 = 4C3 = 4

For two sizes the total for the different color =
`4*2=8`

We can group these like - Same size same color package:

There are eight combinations

Size 1:

BBB

GGG

YYY

PPP

Size 2:

BBB

GGG

YYY

PPP

Next groups form like : Same size different color

Size 1:

BGY

BYP

GYP

BGP

Size 2:

BGY

BYP

GYP

BGP

So, we get total =
`8+8=16`