Question

Three squares of normal chess board are chosed. The probability of getting two squares of one colour and the other of different colour is?

• A. $\frac{16}{21}$
• B. $\frac{8}{21}$
• C. $\frac{8}{64\times 63\times 62}$
• D. $\frac{7}{21}$

Answer 1

The correct option is A $\frac{16}{21}$

No. of ways of selecting $3$ boxes from chess board $={}^{64}{C}_3$

(since chess board is $8\times 8$ bones )

No. of ways of selecting $\to$ two bones of same colour

$={}^{32}{C}_2$

No. of ways of selecting $\to$ one box of other colour

${}^{32}{C}_1$

So, probability $=\frac{{}^{32}{C}_2\times {}^{32}{C}_1\times 2}{{}^{64}{C}_3}$

[multiple by two since there are two different colour]

$=\frac{16}{21}$