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Question
Three squares of chessboard are selected at random. The probability of getting 2 squares of one colour and other of a different colour is ______.
Options
`16/21`
`8/21`
`3/32`
`3/8`
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Solution
Three squares of chessboard are selected at random. The probability of getting 2 squares of one colour and other of a different colour is `16/21`.
Explanation:
In a chessboard, there are 64 squares of which 32 are white and 32 are black.
Since 2 of one colour and 1 of other can be 2W, 1B, or 1W, 2B, the number of ways is (32C2 × 32C1) × 2 and also, the number of ways of choosing any 3 boxes is 64C3.
Hence, the required probability = `(""^32C_2 xx ""^32C_1 xx 2)/(""^64C_3)`
= `16/21`.
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