A cube having all of its sides painted is cut by two horizontal, two vertical, and other two planes so as to form 27 cubes all having the same dimensions. Of these cubes, a cube is selected at random. The probability that the cube selected has none of its sides painted isThe probability that the cube selected has two sides painted isThe total number of cubes having at least one of its sides painted is

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1/9

1/27

1/18

5/54

1/9

4/9

8/27

none of these

answer is , , .

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Detailed Solution

Clearly, cube at the centre is the only cube which is not painted.On each edge, we have one cube pained on two sides. So, there are twelve cubes pained on two sides.Clearly, cube at the centre is the only cube which is not painted.On each edge, we have one cube pained on two sides. So, there are twelve cubes pained on two sides.Clearly, cube at the centre is the only cube which is not painted.On each edge, we have one cube pained on two sides. So, there are twelve cubes pained on two sides.

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