In a certain province in France there are 19 cities. If a single road segment connects only two cities, how many road segments are required in order to connect the cities so that each city is connected to all other cities with a single road segment? Choose the most appropriate option.
A) 30
B) 105
C) 330
D) 143
E) 171
1 city needs 18 roads to connect directly to the rest =&gt; 19 city needs 19*18 roads.   One road is counted twice =&gt; the number of road needed is 19*18/2= 
<gadget id="calculator">19*18/2</gadget>
<output>171</output>
171   Answer 171
<result>E</result>
In a certain province in France there are 19 cities. If a single road segment connects only two cities, how many road segments are required in order to connect the cities so that each city is connected to all other cities with a single road segment?