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Question

Three squares of a chess board are chosen at random, the probability that two are of one color and one of another is


A

1621

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B

821

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C

3212

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D

None of these

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Solution

The correct option is A

1621


Explanation for the correct answer:

There are 64 squares on a chess board. 32of which are white and 32are black.

The number of ways of selecting three squares on a chess board are C364

Now there are two ways of selecting 2 squares of same color and 1 square of the other square.

We can choose 2 white squares and 1 black square or 2 black squares and 1 white square.

This can be done in C2×C13232+C2×C13232 ways.

Hence, the Requiredprobability=NumberoffavorableoutcomesNumberoftotaloutcomes

⇒ Requiredprobability=C2×C13232+C2×C13232C364

⇒ Requiredprobability=2×32!2!30!×32!1!31!64!3!61!

⇒ Requiredprobability=32×31×32×664×63×62

⇒ Requiredprobability=1621

Hence, the probability of choosing 2 squares of same color and 1 square of the other square from a chessboard is 1621.

Hence, option A is the correct answer.


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