CAT 2016 Quantitative Ability

Question : 5 of 34

Marks: +1, -0

A cube is painted with red colour and then cut into 64 small identical cubes. If two cubes are picked randomly from the heap of 64 cubes, what is the probability that both of them have exactly two faces painted red?

${23}/{168}$
${47}/{84}$
$1/4$
$3/8$

Validate

Solution:

The number of ways of picking two small cubes

=^{64} {C}_{2}=32×63

The number of small cubes with exactly two facespainted red
= 2 x 12 = 24 (Since two such cubes will be obtainedfrom each edge of the large cube.)
The number of ways of picking two such cubes

=^{24}C_{2}=23×12

So the required probability

=\;\;{23×12}/{63×32}

=\;\;{23}/{168}

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