10 teams containing 2 players each compete in a doubles tennis tournament. After the medal ceremony, every player shakes hands once with every other player except the other member of their team. How many handshakes occur?

So I thought it would be 19*20=380 because there are 20 players and each player shakes 19 hands but that is not correct.

Guest Aug 8, 2022

#1**+2 **

The first team will have a total of 18 + 18 = 2*18 unique handshakes

The second team will have a total of 16 + 16 = 2*16 unique handshakes

The third team will have a total of 14 + 14 = 2*14 unique handshakes

.

.

The ninth team has a total of 2 + 2 = 2 * 2 unique handshakes

So the total = 2 ( sum of the first 9 even positive integers) =

2 (n) (n + 1) =

2 (9) (10) =

180 handshakes

CPhill Aug 8, 2022

#2**0 **

There are \({20 \choose 2} = 190\) ways to choose 2 people to shake hands.

Of these, there are 10 ways to shake hands with the same team member, so there are \(190 - 10 = \color{brown}\boxed{180}\)

BuilderBoi Aug 8, 2022