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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 all the squares in any column are of same order and that of a row are of alternating color is

A

A. `(1 - 1//2^(7))^(8)`

B

B. `1//2^(56)`

C

C. `1 - 1//2^(7)`

D

D. none of these

Text Solution

Verified by Experts

The correct Answer is:
A
The total number of ways of painting first column when colors are not alternating is `2^(8) - 2`. The total number of ways when no column has alternating colors is `(2^(8) - 2)^(8)//2^(24)`.
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