Question: A child paints the six faces of a cube with six different colors red, blue, pink, yellow, green and orange. What is the probability that red, pink and blue faces share a common corner?
A) 1/6
B) 1/20
C) 1/10
D) 1/5
E) None
“A child paints the six faces of a cube with six different” - is a subject covered in the GMAT quantitative reasoning section. A student needs to be knowledgeable in a wide range of qualitative skills in order to successfully complete GMAT Problem Solving questions. There are 31 questions in the GMAT Quant section overall. Calculative mathematical problems must be solved in the GMAT quant topics' problem-solving section using appropriate mathematical skills.
Solutions and Explanation
Approach Solution : 1
How many different ways can the cube be painted in total? Let's redo the face on the front. There are five options for how to paint the back face, four options for the top, three options for the right side, two options for the bottom, and one option for the left side. That's five. If the top, right, bottom, and left were OYGB, however, that would be the same as YGBO, which is the same as GBOY, which is the same as BOYG. Therefore, we must divide 5 by 4. That leaves us with a total of 5 * 3 * 2 = 30 different ways to paint the cube.
We must now determine how many ways there are to "win." Pink must be next to each of the adjacent faces if blue is one of them and red must be next to the other faces if red is the front face. Once the blue has been painted, the pink could be placed on either side of the blue, giving users two options. There are three ways to finish the final three colors. To fill in OYG, there are 3 ways to choose where to put pink, which adds up to 2*3*2=12.
Out of a total of 30 possible outcomes, there are 12 ways to "win". That's 2/5.
Correct Answer: (E)
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