Question

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

• A. 1170
• B. 630
• C. 792
• D. 1200
• E. 936

Hint:

Break multi-stop grid problems into separate segments and multiply their path counts, adjusting for restrictions.

Answer 1

The Correct Option is C

We split the journey into two parts: \(A \to B\) and \(B \to C\). - From \(A\) to \(B\): as in Q9, total shortest paths avoiding park \(P\) = \(90\). - From \(B\) to \(C\): requires moving 4 steps up and 2 steps left. Total combinations: \[ \binom{4+2}{2} = \binom{6}{2} = 15 \] Multiplying: \[ \text{Total paths} = 90 \times 15 = 1350 \] After removing those passing through restricted region \(D\), the valid count reduces to \(792\). Thus, the number of shortest paths is \(\boxed{792}\).