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# Eight people are to be divided into two groups. What is the

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Manager
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Eight people are to be divided into two groups. What is the [#permalink]  17 Jul 2007, 08:07
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Eight people are to be divided into two groups. What is the probability that there will be 4 in each groups?
VP
Joined: 08 Jun 2005
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[#permalink]  17 Jul 2007, 10:24
choices are:

1,7
2,6
3,5
4,4
5,3
6,2
7,1

so the answer should be 1/7

note - 8C4/(2^8) is a number greater then 1 !!! since 2,520/256 is greater then 1.
Senior Manager
Joined: 03 Jun 2007
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[#permalink]  17 Jul 2007, 10:31
KillerSquirrel wrote:
choices are:

1,7
2,6
3,5
4,4
5,3
6,2
7,1

so the answer should be 1/7

note - 8C4/(2^8) is a number greater then 1 !!! since 2,520/256 is greater then 1.

I missed typing the entire response. It is 8C4/(2^8) * 4C4/(2^8)

Also Killer u missed out the possibilities of 0, 8 and 8,0. Moreover u missed out the possibilites of 8 people being divided into more than 2 groups.
VP
Joined: 08 Jun 2005
Posts: 1147
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Kudos [?]: 127 [0], given: 0

[#permalink]  17 Jul 2007, 10:39
dahcrap wrote:

Also Killer u missed out the possibilities of 0, 8 and 8,0. Moreover u missed out the possibilites of 8 people being divided into more than 2 groups.

1. The stem clearly state "Eight people are to be divided into two groups. What is the probability that there will be 4 in each groups?"

2. For me 0,8 means that you don't have two groups only one group of eight people. I don't like philosophical questions. (i.e. "what is a group of people ?").

3. what's the OA.

Senior Manager
Joined: 03 Jun 2007
Posts: 384
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Kudos [?]: 10 [0], given: 0

[#permalink]  17 Jul 2007, 10:57
KillerSquirrel wrote:
dahcrap wrote:

Also Killer u missed out the possibilities of 0, 8 and 8,0. Moreover u missed out the possibilites of 8 people being divided into more than 2 groups.

1. The stem clearly state "Eight people are to be divided into two groups. What is the probability that there will be 4 in each groups?"

2. For me 0,8 means that you don't have two groups only one group of eight people. I don't like philosophical questions. (i.e. "what is a group of people ?").

3. what's the OA.

Sorry for the confusion. I think I explained it the wrong way.

THere is my actual expanation.

Dividing people into 2 groups of 4 requires choosing 4 people from 8. So 8C4 is the number of the ways of forming 2 groups of 4. So far so good.

Now for the total number of ways of forming 2 groups. This can be as you said groups of 1,7, and 7,1 2,6 and 6,2 3,5 and 5,3 4,4 and the philosophical 0,8 and 8,0. Now I feel we need to calculate the number of ways we can get these combinations. So for 1,7 it is 8C1*8C7. Similarly for 2,6 it is 8C2*8C6, for 5,3 it is 8C3*8C5, for 8,0 it is 8C0*8C8 and for 4,4 it is 8C4*8C4

Now on adding these we get (8C1)^2 + (8C2)^2 + (8C3)^2 + (8C4)^2 and the philosophical (8C0)^2

I guess the answer wud be 8C4/((8C1)^2 + (8C2)^2 + (8C3)^2 + (8C4)^2 and the philosophical (8C0)^2)

Now to take it one step further if the order of the groups matters then it is

8C4/2*((8C1)^2 + (8C2)^2 + (8C3)^2 + (8C4)^2 and the philosophical (8C0)^2)
VP
Joined: 08 Jun 2005
Posts: 1147
Followers: 6

Kudos [?]: 127 [0], given: 0

[#permalink]  17 Jul 2007, 11:04
dahcrap wrote:
KillerSquirrel wrote:
dahcrap wrote:

Also Killer u missed out the possibilities of 0, 8 and 8,0. Moreover u missed out the possibilites of 8 people being divided into more than 2 groups.

1. The stem clearly state "Eight people are to be divided into two groups. What is the probability that there will be 4 in each groups?"

2. For me 0,8 means that you don't have two groups only one group of eight people. I don't like philosophical questions. (i.e. "what is a group of people ?").

3. what's the OA.

Sorry for the confusion. I think I explained it the wrong way.

THere is my actual expanation.

Dividing people into 2 groups of 4 requires choosing 4 people from 8. So 8C4 is the number of the ways of forming 2 groups of 4. So far so good.

Now for the total number of ways of forming 2 groups. This can be as you said groups of 1,7, and 7,1 2,6 and 6,2 3,5 and 5,3 4,4 and the philosophical 0,8 and 8,0. Now I feel we need to calculate the number of ways we can get these combinations. So for 1,7 it is 8C1*8C7. Similarly for 2,6 it is 8C2*8C6, for 5,3 it is 8C3*8C5, for 8,0 it is 8C0*8C8 and for 4,4 it is 8C4*8C4

Now on adding these we get (8C1)^2 + (8C2)^2 + (8C3)^2 + (8C4)^2 and the philosophical (8C0)^2

I guess the answer wud be 8C4/((8C1)^2 + (8C2)^2 + (8C3)^2 + (8C4)^2 and the philosophical (8C0)^2)

Now to take it one step further if the order of the groups matters then it is

8C4/2*((8C1)^2 + (8C2)^2 + (8C3)^2 + (8C4)^2 and the philosophical (8C0)^2)

Hello dahcrap - I like your thinking but I recommend that you will use the "occam's razor" on this one - don't forget you have only two minutes !!!

Senior Manager
Joined: 03 Jun 2007
Posts: 384
Followers: 2

Kudos [?]: 10 [0], given: 0

[#permalink]  17 Jul 2007, 11:09
KillerSquirrel wrote:
dahcrap wrote:
KillerSquirrel wrote:
dahcrap wrote:

Also Killer u missed out the possibilities of 0, 8 and 8,0. Moreover u missed out the possibilites of 8 people being divided into more than 2 groups.

1. The stem clearly state "Eight people are to be divided into two groups. What is the probability that there will be 4 in each groups?"

2. For me 0,8 means that you don't have two groups only one group of eight people. I don't like philosophical questions. (i.e. "what is a group of people ?").

3. what's the OA.

Sorry for the confusion. I think I explained it the wrong way.

THere is my actual expanation.

Dividing people into 2 groups of 4 requires choosing 4 people from 8. So 8C4 is the number of the ways of forming 2 groups of 4. So far so good.

Now for the total number of ways of forming 2 groups. This can be as you said groups of 1,7, and 7,1 2,6 and 6,2 3,5 and 5,3 4,4 and the philosophical 0,8 and 8,0. Now I feel we need to calculate the number of ways we can get these combinations. So for 1,7 it is 8C1*8C7. Similarly for 2,6 it is 8C2*8C6, for 5,3 it is 8C3*8C5, for 8,0 it is 8C0*8C8 and for 4,4 it is 8C4*8C4

Now on adding these we get (8C1)^2 + (8C2)^2 + (8C3)^2 + (8C4)^2 and the philosophical (8C0)^2

I guess the answer wud be 8C4/((8C1)^2 + (8C2)^2 + (8C3)^2 + (8C4)^2 and the philosophical (8C0)^2)

Now to take it one step further if the order of the groups matters then it is

8C4/2*((8C1)^2 + (8C2)^2 + (8C3)^2 + (8C4)^2 and the philosophical (8C0)^2)

Hello dahcrap - I like your thinking but I recommend that you will use the "occam's razor" on this one - don't forget you have only two minutes !!!

I hope we dont get these monsters in the actual test. Now Ajay_GMAt can u post the OA and OE.
VP
Joined: 08 Jun 2005
Posts: 1147
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Kudos [?]: 127 [0], given: 0

[#permalink]  17 Jul 2007, 11:13
dahcrap wrote:

I hope we dont get these monsters in the actual test. Now Ajay_GMAt can u post the OA and OE.

I don't think there is an OA or OE for that one. This isn't a GMAT type question. I guess It's from some kind of math text book.

Manager
Joined: 14 Mar 2007
Posts: 62
Followers: 1

Kudos [?]: 1 [0], given: 0

[#permalink]  17 Jul 2007, 23:42
the OA is 35/81 .. source : PS.zip got from the GMAT club forum
Manager
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[#permalink]  22 Jul 2007, 06:37
dahcrap wrote:
ajay_gmat wrote:
the OA is 35/81 .. source : PS.zip got from the GMAT club forum

I am stumped to say the least

There are four different ways:

1, 7
2, 6
3, 5
4, 4

So the answer is 8C4/(8C4+8C3+8C2+8C1)=35/81
[#permalink] 22 Jul 2007, 06:37
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# Eight people are to be divided into two groups. What is the

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