Rami is painting decorative boxes. For each box he paints the lid

Question

Rami is painting decorative boxes. For each box he paints the lid in one color, the 4 sides in a different color, and the base in another different color. Rami has the colors red, blue, green, orange and purple available. How many different possible color schemes are there for Rami to paint each box with using these colors and rules?

(A) 10

(B) 12

(C) 60

(D) 120

(E) 125

(A) 10

(B) 12

(C) 60

(D) 120

(E) 125

MahmoudFawzy · Answer

we have  5  colors from which we will choose  3  to color the box.
the number of ways we can choose  3  out of  5   = 5C3 = 10

Upon choosing the  3  colors for the lid,body and base,
there is  3!  ways to rearrange the colors (because we can't repeat a color)  = 6

total possibilities  = 10*6 = 60

IanStewart · Answer

He has 5 choices for the colour of the lid, then 4 choices for the colour of the sides, then 3 choices for the colour of the base, for (5)(4)(3) = 60 choices altogether.

unraveled · Answer

How do we know that only three colors that are required to paint.?

I understood as per question that since there are six sides of a box each side would be of different color. But after knowing that only five are available felt surely something was wrong with what i comprehended from question but i could never realize that our sides (vertical sides) have same color. Rather i thought within themselves they have color difference and the top and bottom horizontal sides' color has nothing to do with colors on vertical sides.
Thus, i reached to a solution = 5 * (5 * 4 * 3 * 2) * 5

But no answer choices was such a big value.

Where did miss.?

Peddi · Answer

Hi inm87 , in question they told top portion requires one different colour , and sides around(4sides) require one different colour and bottom portion required one different colour, starting with top we have 5 ways to choose , for around 4 sides there are four ways to choose and for the bottom we are left with 3 ways total no of ways = 5*4*3= 60

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IanStewart · Answer

It's the middle of this sentence that tells us the four sides will be painted using just one color:

Since it uses the singular, "a different color", we are using a single color for all four sides. If we were using different colors for each side, it would need to say "he paints... the 4 sides in different colors" or something similar.

So it's a much easier question than the one you were trying to solve -- the question you were solving is potentially quite difficult, depending on how it's worded (the wording would be very important), since you might need to use circular permutations if you're only supposed to think of two boxes as being different if you can't rotate one box to match the other.

unraveled · Answer

Ah.. that realized a little later. Comprehension is going to kill me, my quant is so much affected for that reason only.
Thanks for clarifying...!!

So it's a much easier question than the one you were trying to solve -- the question you were solving is potentially quite difficult, depending on how it's worded (the wording would be very important), since you might need to use circular permutations if you're only supposed to think of  two boxes as being different if you can't rotate one box to match the other .

For circularity would it not be that that "5*5*4*3*2*" should be divided by 4!...
 
Could not understand the text in red. Could you please elaborate.?

ScottTargetTestPrep · Answer

Since there are a total of 5 colors and order matters, the total number of ways to paint the boxes using 3 colors is:

5P3 = 5 x 4 x 3 = 60

Answer: C

luisdicampo · Answer

Deconstructing the Question

There are 5 colors available. The lid, sides, and base must all have different colors.

So we are selecting and assigning 3 distinct colors to 3 different positions.

Step-by-step

Choose the color for the lid:

5

choices.

Choose the color for the sides (different from lid):

4

choices.

Choose the color for the base (different from both):

3

choices.

Total number of color schemes:

5 	imes 4 	imes 3 = 60

Answer C

Using combinations :  
 
  Deconstructing the Question

Using combinations, first choose which  3  colors will be used from the  5  available colors. Then assign those  3  chosen colors to the 3 different parts of the box: lid, sides, and base.

Step-by-step

Choose  3  colors out of  5 :

\binom{5}{3} = 10

Now assign those  3  chosen colors to the  3  different positions:

3! = 6

So the total number of color schemes is

\binom{5}{3} \cdot 3! = 10 \cdot 6 = 60

Answer C

Rami is painting decorative boxes. For each box he paints the lid

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Rami is painting decorative boxes. For each box he paints the lid

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