CAT 2008 — QA Question 6
Directions for next 2 questions:
The figure below shows the plan of a town. The streets are at right angles to each other. A rectangular park (P) is situated inside the town with a diagonal road running through it. There is also a prohibited region (D) in the town.
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Neelam rides her bicycle from her house at A to her club at C, via B taking the shortest path. Then the number of possible shortest paths that she can choose is
Answer & solution
1170
- B
630
- C
792
- D
1200
- E
936
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From point A to B, there are 90 paths possible with the minimum distance travelled.
We can travel from B to C in two ways
1. B – K – M – C
To travel from B to K, we have to take 6 roads, out of which one is towards left and 5 are upwards.
There are 6!/(5!×1!) = 6 ways to do this. (Refer to the explanation in the first question of this set.)
2. B – N – C
To travel from B to N, we have to take 7 roads, out of which one is towards left and 6 are upwards.
There are 7!/(6!×1!) = 7 ways to do this.
∴ There are 6 + 7 = 13 ways in which we can travel from B to C.
∴ Overall there are 90 × 13 = 1170 paths possible
Hence, option (a).