A combinatorics problem on connecting the cities

[Vineeth T]

Fifteen cities are planned to be connected in such a way that each city has precisely one road leading to each of five other cities.How many such roads are to be constructed?

This question was asked in a talent test conducted in our school.

 

[Rogerio]

5*15=75 which is not an even number. So it is impossible.

 

[Vineeth T]

5*15=75 which is not an even number. So it is impossible.

Hi! Rogerio
Can you explain me clearly why is it impossible?

 

[mfb]

Assuming that a road always leads from one city to another city, each city has 5 road ends connected to this city, so we have a total of exactly 75 road ends.
Every road has 2 ends - the total number of road ends has to be even. 75 is not even.