Question

On an island there are 7 cities each 2 of them connected by a direct road they are building a 8th city they also want it to connect with the other 7 existing cities how many roads will there be after they build the 8th city

Answer 1

After the 8th city is built there will be 28 roads between the cities

Explanation:

The given parameters are;

The number of cities initially on the island = 7 cities

The number of roads between each 2 cities = 1 road

Therefore, we have the number of roads between the 7 cities are;

7 cities taking 2 at a time = ₇C₂

`_7C_2 = (7!)/((7 - 2)!\cdot 2!) = 21`

The initial number of roads between the 7 cities = 21 roads

The number of roads, 'n' there will be after the 8th city is built is therefore;

`n = _8C_2 = (8!)/((8 - 2)!\cdot 2!) = 28`

The number of roads there will be after the 8th city is built, n = 28 roads.