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young_gun
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In a game of 4 people, how many different 2 versus 2 groups 13 Apr 2008, 08:13
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In a game of 4 people, how many different 2 versus 2 groups can be formed?

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In a game of 4 people, how many different 2 versus 2 groups 13 Apr 2008, 10:12
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There is 3 ways you can choose 2 people from a group of 4. After this choice is made you have two people left (therefore the other team is already chosen)

so there is 3 ways in which you can choose 2vs2 teams out of 4 people.

The long way:

Given A,B,C,D

AB Vs CD
AC Vs BD
AD Vs BC

there is no other way you can choose the teams
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In a game of 4 people, how many different 2 versus 2 groups 13 Apr 2008, 10:43
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buffdaddy
There is 3 ways you can choose 2 people from a group of 4. After this choice is made you have two people left (therefore the other team is already chosen)

so there is 3 ways in which you can choose 2vs2 teams out of 4 people.

The long way:

Given A,B,C,D

AB Vs CD
AC Vs BD
AD Vs BC

there is no other way you can choose the teams
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How would you do a more difficult problem such as:
In a group of 8 people, how many different 4 versus 4 teams could you form? thx

Can someone tell my why 4C2 * 2C2 = 6, is not the correct answer?
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In a game of 4 people, how many different 2 versus 2 groups 13 Apr 2008, 13:39
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young_gun

Can someone tell my why 4C2 * 2C2 = 6, is not the correct answer?
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ok lets see
4C2 = the number of ways you can choose 2 from 4 people = 6 (the total number of teams)
BUT a team containing a certain teammember cannot play another team containing the same team member, eg AB cannot play AC,AD,BC, BD since A and B are unique.

So out of 6 teams, there can be 6C2 = 15 combinations of 2 teams (to play against each other). BUT since some teams cannot play each other (unless we clone individuals :-)) we have to divide this number by 5 (the number of teams with either player X or Y)


young_gun

How would you do a more difficult problem such as:
In a group of 8 people, how many different 4 versus 4 teams could you form? thx
Show more

in the same was as above 8C4 gives 70 teams. Divide this by 2 gives the 35 possible matchups
(i am not 100% sure about this scenario, maybe a math maestro like Walker can shed some light)



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