Question

A cube with all the six faces coloured is cut into 64 cubical blocks of same size which are throughly mixed. Two blocks are now selected at random. The probability that both of these blocks have exactly two coloured is

• A. $\frac{21}{68}$
• B. $\frac{25}{68}$
• C. $\frac{23}{168}$
• D. None of these

Answer 1

The correct option is C $\frac{23}{168}$

exactly two faces are colored when box are present at the edges and not at the corner
n(E) = 12+8+12 - 8 = 24
n(S) = 64
P = $\frac{{}^{24}{C}_2}{{}^{64}{C}_2}=\frac{23}{168}$