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Dividing a team

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SVP
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Joined: 16 Oct 2003
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Dividing a team [#permalink] New post 30 Aug 2004, 12:46
Here are two question which I was having problem with and AkamaiBrah explained it well. Please try

1. In how many ways can 12 students be partitioned into 3 teams, A, B, and C, so that each team contains 4 students?

2. In how many ways can 12 students be divided into 3 teams of 4 people each?
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 [#permalink] New post 30 Aug 2004, 12:55
12C4+8C4+4C4

495+70+1

566
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 [#permalink] New post 30 Aug 2004, 13:03
There is a subtly here,

In the first one, the answer is 12C4 * 8C4 * 4C4

How many ways you can pick 4 for team A, times the ways you can pick 4 for team B, times the ways you can pick 4 for team C.

In the second one, the teams are unnamed, hence the following assignment

p1 p2 p3 p4 p5 p6 p7 p8 p8 p10 p11 p12

is the same as

p5 p6 p7 p8 p8 p10 p11 p12 p1 p2 p3 p4

so you need to divide the result of the first question by 6, to account for all the sequences that give you the same result.
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 [#permalink] New post 30 Aug 2004, 13:07
SigEp....does *=multiplication? Wouldn't you add the combinations together?
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 [#permalink] New post 30 Aug 2004, 15:08
Definately Multiple. For each assignment to the first group, you multiply by the ways you can form the second (and so on) groups.
  [#permalink] 30 Aug 2004, 15:08
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Dividing a team

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