Unique Paths

A robot on an m x n grid starts at top-left and can only move right or down. How many unique paths exist to the bottom-right?

Input:

3 7

Output:

Reasoning:

The grid size is determined by the input values, with $m = 3$ rows and $n = 7$ columns.
To reach the bottom-right corner, the robot must make $m - 1 = 2$ moves down and $n - 1 = 6$ moves right, for a total of $m + n - 2 = 8$ moves.
The number of unique paths is equivalent to choosing $m - 1 = 2$ moves down out of the total $8$ moves, which can be calculated using the binomial coefficient: $\binom{8}{2} = \frac{8!}{2!(8-2)!} = \frac{8 \cdot 7}{2} = 28$ .
The final output is the result of this calculation, which represents the total number of unique paths to the bottom-right corner.