# Not a Chessboard

**Discrete Mathematics**Level 5

Calvin fills in a \(7\times7\) grid with the numbers \(1\) through \(49\) in a random arrangement. He then erases his work and does the same thing again, to obtain two different random arrangements of the numbers in the grid. What is the expected number of pairs of numbers that occur in either the same row as each other or the same column as each other in both of the two arrangements?