Question

If there are 12 people sitting at a round table , how many different pairs of people can have conversations during dinner, assuming the can all talk to each other? What geometric figure can you use t model this situation?

Answer 1

66 different pairs. Use a dodecagon showing sides and angles

Answer 2

Answer:

Step-by-step explanation:

Given that there are 12 people sitting around at a table.

We see that any two persons can have conversations.  If we count A with B as one conversation this is the same as B with A

i.e. order does not matter

So here we have to use combinations.

2 people out of 12 where order does not matter can be done in 12C2 ways

No of conversations = $12C2\\= \frac{12!}{2!10!} \\=66$

If we use a dodedecon as a geometrical figure with 12 vertices representing 12 persons the conversation between pairs can be associated with all diagonals and sides connecting two vertices.

Sides are 12 and diagonals are 54 totalling 66.