How many possible conversations are there in a room with 12 people?

There would be 66 possible conversations between two people.

The theory for this question is here

https://en.wikipedia.org/wiki/1_%2B_2_%2B_3_%2B_4_%2B_%C2%B7_%C2%B7_%C2%B7

This question is referred to as the handshake problem", because that is the more common way to ask how many ways a certain number of people can be made into pairs. The answer is to add up 1+2+3+...+(n-1), where n is the number of people involved. In this case, the sum of 1+2+3+4+5+6+7+8+9+10+11 gives 66. The mathematical basis is as given in the previous link.

http://www.scientificpsychic.com/mind/party1.html

It has been pointed out that conversations, unlike handshakes, can involve more than two people at a time. This means that a complete answer must calculate the sum if you include 2 at a time (66 possibilities, as previously explained) + 3 at a time (220 possibilities, calculated as 12C3) + 4 at a time (12C4 = 495 possibilities) + 5 at a time (12C5 = 792 possibilities) + 6 at a time (12C6 = 924 possibilities) + 7 at a time (12C7 = 796 possibilities) + 8 at a time (12C8 = 495) + 9 at a time (12C9 = 220) + 10 at a time (12C10 = 66) + 11 at a time (12C11 = 12) + all 12 at once (12C12 = 1). this gives a grand total of 4073. If people muttering to themselves counts as a conversation, the answer would be 4085.

https://en.wikipedia.org/wiki/Combination

And, people could also be conversing on their cell phones.