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

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There are 2 size options: small and large.abhasjha 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 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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There are two different cases to consider:A certain office supply store stocks 2 sizes of stick notepads,each in 4 colours : blue,green,yellow or pink.The store packs the note pads in packages that contain either 3 notepads of the same size and the same colour or 3 notepads of the same size and different colours.If the order in which the colours are packed doesnt matter,how many different packages of the types described above are possible?

a)6

b)8

c)16

d)24

e)32

Thanks

1) All 3 pads the same color

2) The 3 pads are 3 different colors

**Case 1: All 3 pads the same color**

Take the task of packaging pads and break it into stages.

Stage 1: Select a size

There are 2 possible sizes, so we can complete stage 1 in 2 ways.

Stage 2: Select 1 color (to be applied to all 3 pads)

There are 4 possible colors from which to choose, so we can complete stage 2 in 4 ways.

By the Fundamental Counting Principle (FCP) we can complete the two stages in (2)(4) ways (=

**8**ways)

**Case 2: The 3 pads are 3 different colors**

Take the task of packaging pads and break it into stages.

Stage 1: Select a size

There are 2 possible sizes, so we can complete stage 1 in 2 ways.

Stage 2: Select 3 different colors

There are 4 possible colors, and we must choose 3 of them.

Since the order of the selected colors does not matter, we can use combinations.

We can select 3 colors from 4 colors in 4C3 ways (4 ways), so we can complete stage 2 in 4 ways.

By the Fundamental Counting Principle (FCP) we can complete the two stages in (2)(4) ways (=

**8**ways)

So, both cases can be completed in a total of

**8**+

**8**ways =[spoiler] 16 = C[/spoiler]

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Answer: Option Cabhasjha 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

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The question is essentially about the Combination Formula and following instructions. However, if you don't realize that, then you can always "brute force" the solution - you just have to draw it all out.

We're told that there are 2 sizes of notepads and 4 colors (Blue, Green, Yellow, Prink) of notepads. For organizational purposes, I'm going to refer to the 8 types of pads as:

B = Big blue pad

b = Little blue pad

G = Big green pad

g = LIttle green pad

Etc.

Now, we just need to figure out how many options fit each description:

1st: 3 notepads of the SAME SIZE and SAME COLOR....

BBB

bbb

GGG

ggg

YYY

yyy

PPP

ppp

8 options

2nd: 3 notepads of the SAME SIZE and 3 DIFFERENT COLORS

BGY

BGP

BYP

GYP

bgy

bgp

byp

gyp

8 options

Total options = 8 + 8 = 16

Final Answer: C

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