Question

Neelam rides her bicycle from her house at \(A\) to her office at \(B\), taking the shortest path. The number of possible shortest paths that she can choose is:

• A. 60
• B. 75
• C. 45
• D. 90
• E. 72

Hint:

In grid path problems with restrictions, use total combinations minus the number of paths through the restricted zone.

Answer 1

The Correct Option is D

From the grid, \(A\) to \(B\) requires 6 moves to the right and 4 moves down. The total number of shortest paths without any restriction is: \[ \binom{6+4}{4} = \binom{10}{4} = 210 \] However, the park \(P\) blocks certain paths. From the figure, \(P\) is a triangular restriction equivalent to blocking 2 shortest paths that pass through it. After excluding these, the valid paths = \(210 - 120 = 90\). Thus, the answer is \(\boxed{90}\).