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Different Views of Looking at a solid

A cube is div...

Question

A cube is divided into 343 identical cubelets. Each cut is made parallel to some surface of the cube. But before donig that cube is colored with green colour on one set of adjacent faces, red on the second and blue on the third set

How many cubelets are colored with exactly two colors?

A

48

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B

36

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C

51

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D

50

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Solution

The correct option is C 51
Number of cubelets with no face painted will

$= {(n - 2)}^{3} = {(7 - 2)}^{3} = 125$

No. of cubelets with 2 color
= Total no. of cubelet - [cubelets with one color + cubelets with no color + cubelets with three color]

= 343 - [125 + 2 + 165] = 51

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