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In how many ways can $8$ people be divided into

  1. $4$ groups of $2$ people

  2. First pair, second pair. Third pair and the fourth pair

How do you go about doing this question?

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Are you familiar with binomial coefficients? What have you tried? –  Jeremy Nov 2 '12 at 9:21
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1 Answer

4 groups of 2 people:

  _ _      _ _      _ _      _ _
( 8.7/2! * 6.5/2! * 4.3/2! * 2.1/2! )/4!

First pair, second pair. Third pair and the fourth pair:

1º pair -> 8*7/2! = 28
2º pair -> 6*5/2! = 15
 ...    ->   ...

understood?

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Use consistent notation, please. –  Cameron Buie Nov 2 '12 at 10:53
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