Count Right-and-Down Grid Routes
Company: Google
Role: Software Engineer
Category: Coding & Algorithms
Difficulty: medium
Interview Round: Other
### Problem
A rectangular grid contains `row_count` rows and `column_count` columns. Starting in its upper-left cell, count the routes that finish in its lower-right cell. A move advances by exactly one cell, either to the right or downward.
Return the number of distinct routes, rather than a particular route. Different orders of moves count separately. The supplied dimensions guarantee a result no larger than `2 * 10^9`.
### Examples
**Example 1**
```text
Input: row_count = 4, column_count = 3
Output: 10
```
Each route has three downward moves and two rightward moves. There are ten possible orders for those moves.
**Example 2**
```text
Input: row_count = 1, column_count = 5
Output: 1
```
With a single row, the only route moves right four times.
### Constraints
- `1 <= row_count <= 100`
- `1 <= column_count <= 100`
- The route count for the supplied grid is at most `2 * 10^9`.
Overview: Count distinct routes through a rectangular grid using only one-cell right and down moves, within the source-guaranteed integer answer bound.