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Question

(A) chessboard has $64$ squares,with $32$ white squares and $32$ black squares.Total ways to choose $3$ squares out of $64$ is ${}^{64}C_3 = \frac{64

Vedclass · Accepted Answer

$\frac{16}{21}$

Vedclass · Answer

(A) chessboard has $64$ squares,with $32$ white squares and $32$ black squares.Total ways to choose $3$ squares out of $64$ is ${}^{64}C_3 = \frac{64 	imes 63 	imes 62}{3 	imes 2 	imes 1} = 41664$.We need to choose two squares of one colour and one of another. This can happen in two ways:$(i)$ Two white and one black: ${}^{32}C_2 	imes {}^{32}C_1 = \frac{32 	imes 31}{2} 	imes 32 = 496 	imes 32 = 15872$.$(ii)$ Two black and one white: ${}^{32}C_2 	imes {}^{32}C_1 = 15872$.Total favourable cases $= 15872 + 15872 = 31744$.Probability $= \frac{31744}{41664} = \frac{16}{21}$.

Three squares of a chessboard are chosen at random. The probability that two are of one colour and one is of another colour is:

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