Probability of 2 out of 300 over 12 5x5 matrixes

Question

There are 300 cards, each with a different number.

There are 12 tables, each which hold 25 cards (5 rows, 5 columns)

If the cards are blindly and randomly placed on each table, what is the probability of two pre-chosen numbers to be next to each other.

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I’d begin to say perhaps the number of tables is irrelevant? Then 5 rows x 60 columns. However that increases the chances of two of the pre-chosen cards sitting together.

Answer 1

Consider the first number, on a single table of 5x5, if that number is placed on the inner 3x3 grid, then for each cell, there are 9 possible ways the other number can be next to this number (i assume diagonal neighbors are valid neighbors). if it is located on the border but not corners, then there will be 5 possibilities and if it is on the corner then only 3, hence the total possible ways will be 9*9 + 12*5+ 4*3 = 153. Now, in how many ways do those 2 numbers end up on the same table? the answer is C(298, 23) and in each case, the probably of having the two next to each other will be 153*298!/300!, and since we have 12 tables, the overall probability will be 153*298!*12/300! = 153*12/(300*299)=0.02