Question

Three squares of a chess board being chosen at random, what is the chance that two are of one colour and one of another?

Answer 1

There are $64$ squares on chess board out of which $32$ are black and $32$ are white

The person can either choose $2$ black $1$ white or $2$ white $1$ black

$\Rightarrow P\left(E\right)=\frac{{}^{32}{C}_2{\times }^{32}{C}_1}{{}^{52}{C}_3}+\frac{{}^{32}{C}_2{\times }^{32}{C}_1}{{}^{52}{C}_3}\Rightarrow P\left(E\right)=2\times \frac{{}^{32}{C}_2{\times }^{32}{C}_1}{{}^{52}{C}_3}=\frac{16}{21}$