Question

On an island there are 7 cities. Each two of them connected by a direct road. How many roads are there?

Answer 1

21 roads

Explanation:

If for each city, there would be 6 direct roads, for example from island 1, there would be 6 direct roads, one for each rest of the island, island 2,3,4,5,6,7.

But the path from island 1 to 2 would be the same as that from island 2 to 1, it would be one less for each island, therefore in total it would be:

6 + 5 + 4 + 3 + 2 + 1 = 21

21 roads in total

Answer 2

21 roads

Explanation:

If each two cities are connected by a direct road, to find the number of roads we just need to solve a combination of 7 choose 2, that is, we need to find all pairs of two cities among the 7 cities:

Combination of 7 choose 2 = 7! / (5! * 2!) = 7*6/2 = 21

So there is a total of 21 roads on the island.