Two lines of a Latin square
Task number: 3901
In how many ways can the first two lines of a Latin square of the order \( n \) be filled in correctly?
The first two lines can be seen as a notation of the permutation. Because two identical symbols must not appear in the same column, this permutation is without fixed points.
However, the first line of each such permutation can be selected in \(n!\) ways.
These two lines can be filled in \(n!\cdot s(n)\) ways, where \(s(n)\) is the function from the cloakroom problem.