Given two positive integers row_count and column_count representing the dimensions of a grid, compute the number of distinct paths from the cell at (0, 0) to the cell at (row_count-1, column_count-1), where movement is restricted to only right or down at each step.
Example 1
Input: row_count=4, column_count=5
Output: 35
Explanation: There are 35 distinct paths from (0,0) to (3,4) moving only right or down.
Example 2
Input: row_count=2, column_count=2
Output: 2
Explanation: There are 2 distinct paths: right->down or down->right.
Constraints
Case 1
Input: row_count=5, column_count=3
Expected: 15
Case 2
Input: row_count=6, column_count=1
Expected: 1
Case 3
Input: row_count=1, column_count=8
Expected: 1
Case 4
Input: row_count=7, column_count=4
Expected: 84