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# How many different ways can a group of 8 be divided into 4

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Intern
Joined: 21 Jan 2006
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How many different ways can a group of 8 be divided into 4 [#permalink]  22 Jan 2006, 08:48
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How many different ways can a group of 8 be divided into 4 teams of 2 people?
Director
Joined: 09 Oct 2005
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the number of ways we can select 2 people from 8 =>2C8=28
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Intern
Joined: 21 Jan 2006
Posts: 19
Location: India
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Ways of selecting first team:

8C2 = 28

2nd team: 6C2 = 15

3rd team: 4C2 = 6

4th team: 2C2 = 1

Therefore, using the multiplication principle, the total number of ways =

28 X 15 X6 X 1 = 2520

However, order of selection does not matter, hence we must divide
this number by the factorial of the number of teams...

Senior Manager
Joined: 11 Jan 2006
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Location: Chennai,India
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21stCenturion wrote:
Ways of selecting first team:

8C2 = 28

2nd team: 6C2 = 15

3rd team: 4C2 = 6

4th team: 2C2 = 1

Therefore, using the multiplication principle, the total number of ways =

28 X 15 X6 X 1 = 2520

However, order of selection does not matter, hence we must divide
this number by the factorial of the number of teams...

had this problem always when do i add n when do i multiple.. pls someone explain!
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Director
Joined: 26 Sep 2005
Posts: 577
Location: Munich,Germany
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I made the same mistake as Andy did.Can someone explain when to add and miltiply..would be helpful
Manager
Joined: 23 Jan 2006
Posts: 192
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Kudos [?]: 12 [0], given: 0

can someone explain this?

Quote:
However, order of selection does not matter, hence we must divide
this number by the factorial of the number of teams...

GMAT Club Legend
Joined: 07 Jul 2004
Posts: 5068
Location: Singapore
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# of ways to get teams of 2 people from a group of 8 peopele = 8C2 = 8!/2!6! = 28
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