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

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Detailed Solution

We begin by remembering that a standard chessboard has

64

squares,

32

of which are of one colour (black), and

32

of which are of a different colour (white). The number of ways to select '

r

' items from '

n

' (nr) items is then recalled to be

rnC

ways. We then incorporate this information into the probability formula: probability of choosing

2

black squares and

1

white square + probability of choosing

1

black square and

2

white square. number of possible ways to select

3

squares from the board's

64

squares in order to obtain the necessary Answer.
The chess board has 64 square in total i.e 32 of black and 32 and white.
Then possible ways

64_{C_{3}}

Favorable ways 2 black

\times

white, 2 white

\times

black

= 32_{C_{2}} \times 32_{C_{1}} + 32_{C_{2}} \times 32_{C_{1}}

= 2 \times 32_{C_{2}} \times 32_{C_{1}}

Probability =

\frac{Favorable}{possible}

= \frac{2 \times 32_{C_{2}} \times 32_{C_{1}}}{64_{C_{3}}}

= \frac{2 \times \frac{32 \times 31}{2} \times 32}{\frac{64 \times 63 \times 62}{6}} = \frac{16}{21}

Hence option (1) is correct.

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