There are 13 train stops between Chennai and Assam. How many train tickets are to be printed, so that a person can travel between any of the two stations (irrespective of direction of travel)?
Question
There are 13 train stops between Chennai and Assam. How many train tickets are to be printed, so that a person can travel between any of the two stations (irrespective of direction of travel)?
Solution
To solve this problem, we need to understand that a person can travel from any station to any other station in both directions. This means that for each station, there are (n-1) possibilities of travel, where n is the total number of stations. However, since each ticket allows travel in both directions, we would be double counting if we simply multiplied the number of stations by (n-1). Therefore, we need to divide by 2 to get the correct answer.
Here are the steps to solve this problem:
- Calculate the total number of possible travels from each station: 13 * (13 - 1) = 156
- Since each ticket allows travel in both directions, divide the total by 2: 156 / 2 = 78
So, 78 train tickets need to be printed so that a person can travel between any of the two stations.
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