UPSC CSE Prelims 2011
Study the following figure:
A person goes from A to B always moving to the right or downwards along the lines. How many different routes can he adopt?
EXPLANATION
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.
