IPMAT Indore 2023 - QA (MCQ) Q20 Explanation

Explanation:

(d)

First rook can be placed in 64 ways i.e. 82 ways. (place it at any of the 64 squares of the chessboard).

Now the second rook should be place such that it should not lie in the same row or column in which the first is placed.

Placing first rook in any of the 64 squares will block 15 squares for other rooks.

So, the second rook can be placed in remaining 49 ways i.e. 7^2 ways. This will block 13 more squares of the chessboard for remaining rooks.

Third rook can be placed in 62 i.e. 36 ways and so on.

Total number of ways = 8^2 × 7^2 × 6^2 × 5^2 × 4^2 × 3^2 × 2^2 × 1^2 = (8!)^2

As all the 8 rooks will be identical, final number of ways = (8!)^2/8! = 8! Ans.