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In how many ways can a group of 8 be divided into 4 teams of

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Senior Manager
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In how many ways can a group of 8 be divided into 4 teams of [#permalink] New post 24 Aug 2007, 08:04
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In how many ways can a group of 8 be divided into 4 teams of 2 each?

A) 90
B) 105
C) 168
D) 420
E) 2520

Please explain!
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 [#permalink] New post 24 Aug 2007, 08:29
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 [#permalink] New post 25 Aug 2007, 02:13
leeye84 wrote:
Thanks!

If the groups were distinguishable, it would be 8C2 x 6C2 x 4X2 = 28 x 15x 6

We need to divide this by the number of ways of labelling the 4 groups: 4!

7 x 15 = 105
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 [#permalink] New post 25 Aug 2007, 03:11
One can also approach it as follows:

The first person has 7 persons to choose from to form a team with.

After the first pair has been formed, there are 6 more people in the group. The first person from this group of 6 will have 5 persons to choose from to form a team with.

Once the second pair is formed, there are 4 more people in the group. The first person in this group of 4 will have 3 persons to choose from to form a team.

Once the third pair is formed, only 2 more people are left with and they have only 1 choice.

Hence the total no. of pairs is 7*5*3*1 = 105
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 [#permalink] New post 25 Aug 2007, 06:34
subhen wrote:
One can also approach it as follows:

The first person has 7 persons to choose from to form a team with.

After the first pair has been formed, there are 6 more people in the group. The first person from this group of 6 will have 5 persons to choose from to form a team with.

Once the second pair is formed, there are 4 more people in the group. The first person in this group of 4 will have 3 persons to choose from to form a team.

Once the third pair is formed, only 2 more people are left with and they have only 1 choice.

Hence the total no. of pairs is 7*5*3*1 = 105


Great explanation :-D
  [#permalink] 25 Aug 2007, 06:34
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