CAT 2008 | Question: 04

Question

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

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

Answer 1

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