A group of 6 girls and 6 boys wants to play volleyball They

A group of 6 girls and 6 boys wants to play volleyball. They have to set up the teams. At first, they decide that the number of boys or girls in a team is not important.

Under the assumption that the part of the court that a team will occupy is relevant,

find the number of different teams they can set up. Total number of ways = 1848

Find the number of different teams they can set up provided that the part of the court that a team will occupy is irrelevant. Total possibility is 1848.

They then decide to set up teams made of 3 girls and 3 boys each. Again, the part of the court that a team will occupy is irrelevant.

Find the number of different possibilities in which the girls can they distribute themselves.

Solution

1-a) in the first question, they just have to set up different teams say A and B. It is like dividing 12 people into 2 groups with 6 in each. which is

12! / (6!6!) =924 now you have to consider the case in which two teams matter. so,

924*2= 1848

or you can solve it like :

you took 12C6*2!(for permutation of 2 teams)

1-b)2nd also doesnot change anything as the court is irrelevant in this division.

6C3*6C3*2!=20*20*2= 800

[note here that I have taken 2 teams different like they are playing for team A and Team B , if this is not the case and you just have to form any random 2 teams which can play against each other then 2! won\'t come into the picture . It will also not be in 1(b), then your ans will be 924 and not 1848]