Question

Decide if true or false:

Please provide some working for me to understand.

A teacher wants to organize a football game with 22 players by grouping them into two teams of equal size. The total number of ways in which the teacher can form the teams is 22!/2.

Answer 1

The given number of ways to form two teams of equal size with 22 players is wrong.Suppose that we want to create two team of 11 player each from 22 players. Then we have to choose 11 players from 22 to create a team. So the number of ways we can create a team is given by   

Now if a team is selected then the other team is itself made with the remaining players. So the other team formed itself also include the previous team. so this include twice time a team So we need to divide it by two.

Hence  the total number of ways to choose two team is