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AP EAMCET202018 Sep 2020Evening ShiftMathematicsProbabilityActual

Three squares of a chessboard are selected at random. The probability of selecting two squares of one colour and the other of a different colour is equal to

Options

  1. A( 10 17 )
  2. B( 15 19 )
  3. C( 17 23 )
  4. D( 16 21 )

Correct answer

D. ( 16 21 )

Step-by-step solution

Total number of ways of selecting 3 square (=64_ C ₃ ) Total number of ways of selecting 2 square of one colour and other square of different colour (=(2 ) white, 1 black () ) or (1 white, 2 black () ) ( aligned & = ³² C ₂ ³² C ₁+ ³² C ₁ ³² C ₂ & =2 32_ C ₂ 32_ C ₁ aligned ) ( aligned Required Probability & = 2.32_ C ₂ 32_ C ₁ 64_ C ₃ & = 2 32 31 2 1 32 64 63 62 3 2 1 = 16 21 aligned ) Hence, option (d) is correct.

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