The problem speaks about distributing 5 identical balls in 3 rows, with the constraint that each row must contain at least one ball. This is a problem of combinatorics, often solved using methods such as permutation and combination.

Option 1: 64, is incorrect because this is 2^6 (2 to the power of 6), which would be correct if there were 6 balls, or 6 locations with no restrictions on how many balls could go in each.

Option 2: 81, is 3^4 (3 to the power of 4) which would be correct if there were no restrictions on the balls, and there were either 4 balls or 4 locations to place them.

Option 3: 84, is incorrect because this number doesn`t represent a simple power situation and doesn`t align neatly with any known combinatorics strategy.

Option 4: 108 which is the correct answer. It refers to the principle of distributing `n` identical items into `r` groups, i.e., the formula for this is (n+r-1)C(r-1). Here n is 5 (balls) and r is 3 (rows), so we get (5+3-1)C(