If the road between to houses is considered as a 'path', at least how many paths are to be made in a city with 20 houses so that it is possible to go to any house from any house?

Question

19-01-2024
Mathematics

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If the road between to houses is considered as a 'path', at least how many paths are to be made in a city with 20 houses so that it is possible to go to any house from any house?

Answer :

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AirDiamond19834 AirDiamond19834 · Answer 1 · 2024-01-19T00:48:30-05:00

Answer:

Step-by-step explanation:

To ensure that it is possible to go to any house from any house in a city with 20 houses using paths, you need to create a direct path between each pair of houses. This means that for each house, there should be a direct route to every other house.

In a city with 20 houses, if you want to create a direct path between each pair of houses, you can use the concept of combinations. The formula for finding the number of paths needed is:

Number of paths = nC2

Where:

n is the total number of houses (20 in this case).

C2 represents "combinations of 2," which calculates the number of ways to choose 2 houses out of the total.

So, for a city with 20 houses:

Number of paths = 20C2 = (20 * 19) / (2 * 1) = 190 paths

You would need to create at least 190 paths in the city to ensure that it is possible to go to any house from any house.