A group of 8 friends wants to play double tennis. How many

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A group of 8 friends wants to play double tennis. How many [#permalink]

08 Jun 2008, 12:03

A group of 8 friends wants to play double tennis. How many different ways can the group be divided into 4 teams of 2 people?

a) 420
b) 2520
c) 168
d) 90
e) 105

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Re: double tennis [#permalink]

08 Jun 2008, 19:36

N=\frac{C^8_2*C^6_2*C^4_2*C^2_2}{P^4_4}=\frac{4*7*3*5*2*3*1}{4*3*2*1}=105
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Re: double tennis [#permalink]

08 Jun 2008, 22:21

walker wrote:

N=\frac{C^8_2*C^6_2*C^4_2*C^2_2}{P^4_4}=\frac{4*7*3*5*2*3*1}{4*3*2*1}=105

Hi Walker,

What is the logic behind 4P4 ?

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Re: double tennis [#permalink]

08 Jun 2008, 22:26

mandy12 wrote:

What is the logic behind 4P4 ?

When we choose four groups, it is necessary to exclude order among groups, for example:

12,34,56,78 and 34,12,56,78 is the same option. (1,2,3,4,5,6,7,8 - people)
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Re: double tennis [#permalink]

08 Jun 2008, 22:30

Can u explain the logic behind this formula?

walker wrote:

N=\frac{C^8_2*C^6_2*C^4_2*C^2_2}{P^4_4}=\frac{4*7*3*5*2*3*1}{4*3*2*1}=105

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Re: double tennis [#permalink]

08 Jun 2008, 22:33

C^8_2 - choose first team

C^6_2 - choose second team

C^4_2 - choose third team

C^2_2 - choose fourth team

P^4_4 - exclude order among four teams.
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Re: double tennis [#permalink]

08 Jun 2008, 22:54

Pretty good explanation Walker
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Re: double tennis [#permalink]

09 Jun 2008, 12:55

for some reason i get 115..

i did as follows.. [8C2*6C2*4C2*2C2]/4!

i use 4! because suppose each player is a nd B..then we have counted that pair twice i.e ab, ba etc for each of the 4 slots..

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Re: double tennis [#permalink]

13 Jun 2008, 08:09

maybe I'm not so skilled in combinative formulas but for me this is the way: for even N the quantity of pairs = (N-1)*(N-3)*...*(N-n), where n = N-1. So that for 8 players it's 7*5*3*1=105. For N=10 it's 9*7*5*3*1 = 945
P.S. I should explain how I reached that. I draw a picture with 4 lines then investigated those combinations, it was 3. Why 3, cause if we chosen 1 pair only 1 pair left. How many first pairs I could chose - 3 (N-1).
OK, how about 6? I chosen 1 pair and what I saw, right, 4 lines. I had already seen them and knew that they consisted 3 possible pairs. How many first pairs I might chose, correct, 5 (N-1). So that we had (N-5)*(N-3)*(N-1). I kept reasoning and found the regularity and wrote it in the opposite way - see above 8-)

.
All this reasoning took around 1 minute...

Re: double tennis [#permalink] 13 Jun 2008, 08:09

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A group of 8 friends wants to play double tennis. How many

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A group of 8 friends wants to play double tennis. How many

A group of 8 friends wants to play double tennis. How many

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