Combinatorics: Chess Board Example - Forbidden Positions

Question

I am struggling to answer the question below and I don't have any idea how I would prove this after getting the answer. Could someone help please? Thanks

In how many ways can 6 non-attacking rooks be placed on a 7x7 chessboard, with forbidden positions being the diagonal line from the top left corner to the bottom right corner (so 7 forbidden positions)? (Caution: we are asking for 6 non-attacking rooks, not 7). Write your answer in terms of derangement numbers and prove that your answer is correct (Proof has to be either using induction or a combinatorics proving method).

Answer 1

Hint: You want a permutation that is either:
1. A complete derangement -> How many are there? How many formations does each permutation yield?
2. Have 1 fixed point, the rest is a derangement -> How many are there? How many formations does each permutation yield?

Hence, there are "Fill this in yourself" formations

Now, prove that any formation satisfying your conditions must satisfy either one of the above conditions.