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Direction for the question given below

The figure below shows the plan of a town. The streets are at right angles to each other. A rectangular park $\text{(P)}$ is situated inside the town with a diagonal road running through it. There is also a prohibited region $\text{(D)}$ in the town

Neelam resides her bicycle from her house at $\text{A}$ to her club at $\text{C,}$ via $\text{B,}$ taking the shortest path, then the number of possible shortest paths that she can choose is

1. $1170$
2. $630$
3. $792$
4. $1200$
5. $936$

Answer $630$

from A robot can go $\text{(d,d,r,r)}$ [d=down, r=right] $= 4!/2!2!$

then go to P line in $1$ way

then ending point of P to B $\text{(d,d,r,r,r,r)} = 6! / 4!2!$

then upwards B to E $\text{(u,u,u,u,u,u,r)} = 7! / 6!$

then E to A $1$ way

total $4! / 2!2! \times 1 \times 6! / 4!2! \times 7! / 6! \times 1 = 630$

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