In a certain province in Italy there are 15 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 correct choice from the following options
A) 30
B) 105
C) 330
D) 14!
E) 15!
Method-1:   Italy Total Cities = 15 and each city should be connected with every other city   So Total Roads required to connect 1st City with other 14 cities = 14   Now 1st City is connected with all other cities so,   So Total Roads required to connect 2nd City with 13 cities (Other than 1st) = 13   Now 1st and 2nd Cities are connected with all other cities so,   So Total Roads required to connect 3rd City with 12 cities (Other than 1st, and 2nd) = 12   ......and so on...   Total Roads required = 14 + 13 + 12 + 11 + 10 + 9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1= 
<gadget id="calculator">14 + 13 + 12 + 11 + 10 + 9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1</gadget>
<output>105</output>
105=105
<result>B</result>
In a certain province in Italy there are 15 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?