QUESTION

CSAT

Hard

Maths

Prelims 2014

With reference to the figure given below number of different routes from S to T without retracing from U and/or V (T is the next node after V), is

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Explanation

To determine the total number of different routes from S to T, we multiply the number of possible paths at each stage.

From S to U, there are 3 possible paths. From U to V, there are 2 possible paths. Since every path from S to U must continue through one of these, the total ways to reach V from S is: $3 \times 2 = 6$ . From V to T, there are 3 possible paths. Extending the logic further, every route from S to V must continue through one of these paths, leading to: $6 \times 3 = 18$ . Thus, the total number of different routes from S to T is 18.