8 x 8 chessboard

[Zelda22]

You are given an 8 x 8 chessboard and eight indistinguishable chechers.
In how many ways can you place the checker on the board so that each row and each column contains exactly one checker?

I'm not sure is this is correct.

1 row-1 column I have 8 x 8 options
2 row-2 column I have 7 x 7 options
3 row-3 column I have 6 x 6 options
4 row-4 column I have 5 x 5 options
5 row-5 column I have 4 x 4 options
6 row-6 column I have 3 x 3 options
7 row-7 column I have 2 x 2 options
8 row-8 column I have 1 x 1 option

So, I have 8! ^ 2 to choose from
and since there is no distinction between the checkers, I have 8! checkers to place.

(8!)^2 / 8!
=8! x 8! / 8!
= 8!
= 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1
=40320

Can you please explain how to solve this question? Thanks

 

[pka]

[imath]\large{8!}[/imath] is correct.

 

[Zelda22]

[imath]\large{8!}[/imath] is correct.

[imath]\large{8!}[/imath] is correct.

Thanks.