Correct Option (3)
The problem requires determining the total number of distinct routes from point A to point B, strictly adhering to movements either to the right or downwards along the designated lines. A systematic enumeration of all permissible paths reveals the following six distinct routes:
- Path 1: A → 1 → 4 → 5 → B
- Path 2: A → 1 → 4 → 7 → B
- Path 3: A → 1 → 2 → 5 → B
- Path 4: A → 3 → 6 → 7 → B
- Path 5: A → 3 → 4 → 5 → B
- Path 6: A → 3 → 4 → 7 → B
Each listed route complies with the specified constraint of moving exclusively right or downwards. Consequently, there are six different routes available.
Incorrect Options:
Options 1 (4), 2 (5), and 4 (7) are incorrect because a complete and accurate enumeration of all possible routes, while adhering to the given movement restrictions, yields a total of six distinct paths, as demonstrated above.
