Answer:
162
Explanation:
3 teams of 4 players each means 12 players altogether.
1. Shaking hands with people of other teams.
Let's call the teams A, B, and C.
1 player of team A shakes hands once with 8 players of teams B and C.
That is 8 hand shakes.
Now each of the other 3 players in team A does the same. That is another 3 × 8 handshakes, or 24 more. So far there are 32 handshakes.
For all players of 1 team to handshake once with each player of the other teams, there are 32 handshakes.
Since there are 3 teams, now the player of team B do the same. This is another 32 handshakes. The players of team C do the same. Another 32 handshakes.
3 × 32 = 96
Since each handshake involves two people, player 1 shaking hands with player 2, and player 2 shaking hands with player 1 is the same handshake, so we must divide 96 y 2 to eliminate the duplicate handshakes.
96/2 = 48
48 is the number of handshakes between each player and the players of the other teams if they shake hands only once, but since when they shake hands with players of other teams, they shake hands 3 times, then we multiply 48 by 3.
48 × 3 = 144
The number of handshakes that take place between a player and the players of other teams is 144.
2. Shaking hands with players of the same team.
Each team has 4 players. Each of the 4 players shakes hands with 3 other players.
4 × 3 = 12, but since each handshake is between two players, and player 1 handshaking player 2 is the same as player 2 handshaking player 1, we divide 12 by 2 to get 6. Within a team, there are 6 handshakes. There are 3 teams, so 3 × 6 = 18.
The number of handshakes that take place within the teams is 18.
Total
144 + 18 = 162