In how many ways can we fill a \(3 \times 5\) board with integers from \(1 \text{ to } 15\) such that the following conditions hold?

- Each integer is used exactly once.
- In all the rows, the sum of all the numbers in the row are equal.
- In all the columns, the sum of all the numbers in the column are equal.

**Also:**

- All permutations of rows or columns count as distinct.
- Transposing the board is not allowed.

**Explicit example:**

\[\begin{bmatrix} 1 & 3 & 11 & 12 & 13 \\ 8 & 7 & 9 & 10 & 6 \\ 15 & 14 & 4 & 2 & 5 \end{bmatrix}\]

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