Question

. In how many ways can four distinguishable pieces be placed on an 8 × 8 chessboard so that no
two pieces are in the same row or column?
A.
8!
4!
. B.
(8!)2
(4!)
. C.
(8!)
(4!)2
. D.
(8!)2
(4!)2
.

Answer 1

Alternatively, we first choose 4 rows and 4 columns which can be done in (8/4)(8/4) ways.

Now as the pieces are distinct, we decide their order in rows in 4! ways and for each such order, we have 4! ways of ordering them in columns.

So total number of arrangements =4! 4!(8/4)(8/4)