Peaceful Party

The mayor of your city has decided to throw a party to gather the favour of his people in different regions of the city. There are $3$ distinct regions in the city namely $A$, $B$, $C$ comprising of $P_A$, $P_B$ and $P_C$ number of people respectively. However, the mayor knows that people of the region $B$ are in conflict with people of regions $A$ and $C$. So, there will be a conflict if peop