if there are 20 people sitting around a table, how many different pairs of people can have conversations...?

Question

if there are 20 people sitting around a table, how many different pairs of people can have conversations during diner? what geometric figures can you use to model people and two-person conversations?

Answer 1

Suppose you have two people. That's one conversation. If you have three people, then three conversations can result (a+b, b+c and a+c; 3=1+2). If you have four people, then six conversations can result (6=1+2+3). If you have five people, then ten can result (1+2+3+4). So if you have twenty people, then 190 conversations can result (1+2+3+4+5+...+16+17+18+19).

So the number of two-person conversations that can result out of X number of people can be determined by summing up the first X-1 positive integers. There's a way to express that mathematically using the sigma symbol, but I never got that far in math, and anyway it would be hard to express in a text medium that doesn't easily lend itself to composition of mathematical equations.

Answer 2

People Sitting Around A Table

Answer 3

20 / 2 =10 pairs

Answer 4

20*19 = 380
You have 20 possibilities to choose the first person for the pair. Once that person has been chosen, you have 19 remaining from which to choose the second person for your pair. You can choose any one of those 19 for each of the 20 you chose for the first of the pair, so 20 * 19.

Answer 5

10 people

Answer 6

20?

Answer 7

Ten pairs.

Answer 8

1 speech is going on. the rest listens.... He's the boss.

Answer 9

It depends. Are they women or men?

Answer 10

10 line .........