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Question: Three squares of a chess board are chosen at random, the probability that two are of one colour and...

Three squares of a chess board are chosen at random, the

probability that two are of one colour and one of another is –

A

16/21

B

8/21

C

32/12

D

None of these

Answer

16/21

Explanation

Solution

Three squares can be chosen out of 64 squares in 64C3 ways. Two squares of one colour and one another colour can be chosen in two mutually exclusive ways :

(i) Two white and one black and

(ii) Two black and one white. Thus the favourable number of cases = 32C2 × 32C1 + 32C1 × 32C2

Hence the required probability

= 2(32C1⋅32C2)64C3\frac { 2 \left( { } ^ { 32 } \mathrm { C } _ { 1 } \cdot { } ^ { 32 } \mathrm { C } _ { 2 } \right) } { { } ^ { 64 } \mathrm { C } _ { 3 } } =1621\frac { 16 } { 21 }