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If the squares of a 8 xx 8 chessboard a...

If the squares of a `8 xx 8` chessboard are painted either red or black at random.
The probability that not all the squares in any column are alternating in color is

A

`(.^(64)C_(32))/(2^(64))`

B

`(64!)/(32!.2^(64))`

C

`(2^(32) - 1)/(2^(64))`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
A
The number of ways the square has equal number of red and black square is `.^(64)C_(32)`. Hence, the required probability is `.^(64)C_(32)//2^(64)`.
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