Question

the 1 st piece can be placed in 64 ways, but 1
row & 1 column get eliminated so the next
piece can only be placed in 49 ways, & so on
[
8^{2} times 7^{2} times 6^{2} times 4^{2}=(8 mathrm{P} 4)^{2}=(8 ! / 4 !)^{2}<
]

# In how many ways can four distinguishable pieces be placed on an 8 x 8 chessboard so that no two pieces are in the same row or column?

Solution