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# In how many ways 12 different things can be divided equally

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Director
Joined: 07 Jun 2004
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Location: PA
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In how many ways 12 different things can be divided equally [#permalink]  12 Jan 2005, 17:30
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Question Stats:

100% (01:07) correct 0% (00:00) wrong based on 0 sessions
In how many ways 12 different things can be divided equally among 3 people.

The answer is in Factorial form.
VP
Joined: 18 Nov 2004
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Gp of 4 things has to be created....so total gps that can be formed = 12C4 = 495 gps

Now select these gps for 3 ppl ==> 495 x 494 x 493 ==> 495! / 492 !

Ans: 495! / 492 !....is that correct ?
Senior Manager
Joined: 22 Jun 2004
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Re: PS: Another counting problem [#permalink]  13 Jan 2005, 00:05

12 different things have to be divided among 3 people.

The number of ways the first guy can order 4 out of 12 is 12p4
The number of ways the second guy can order 4 out of 8 is 8p4
The number of ways the third guy can order 4 out of 4 is 4p4

The total number of ways 12 different things can be divided equally among 3 people is = 12p4 * 8p4 * 4p4 = 12!

rxs0005 wrote:
In how many ways 12 different things can be divided equally among 3 people.

The answer is in Factorial form.

_________________

Awaiting response,

Thnx & Rgds,
Chandra

Director
Joined: 07 Jun 2004
Posts: 614
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Kudos [?]: 270 [0], given: 22

This one sounds tricky but the math is simple

the first set of 4 things can be picked in

12C4 ways so remaining is 8 that can be picked in 8C4 ways and the last 4 can be chosen in 4C4 ways

so total number of ways are

12C4 * 8C4 * 4C4 = 12! / ( 4!) ^ 3
Director
Joined: 31 Aug 2004
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rxs,

Thank you for this question. I was wondering why the answer is not the basic "12C8.8C4.4C4/3!"as there are only 3 people to divide the things in ?
Senior Manager
Joined: 22 Jun 2004
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Hi twixt,

You may not like to divide because the number of ways of division is important among 3. i.e., order is important .So, no division with 3! However, there is no order within the lot of 4 picked up.

Hope I made some sense here!!

twixt wrote:
rxs,

Thank you for this question. I was wondering why the answer is not the basic "12C8.8C4.4C4/3!"as there are only 3 people to divide the things in ?

_________________

Awaiting response,

Thnx & Rgds,
Chandra

Director
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Hi Malellac,

My vision was the opposite as people here are not distinct...
Senior Manager
Joined: 22 Jun 2004
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Hi twixt,

As per my tutor (long time back), people are always distinct in probability unelss the stem says that the people wear masks and thus look alike or something like that.

So, I follow it always. Do let me know your opinion on this.

twixt wrote:
Hi Malellac,

My vision was the opposite as people here are not distinct...

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Awaiting response,

Thnx & Rgds,
Chandra

Director
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My opinion is not as strutured as yours !

The way I consider this distinct/non distinct stuff is for instance :

X items into 3 groups : non distincts then divide by 3!
X items into 3 groups named A B and C : distinct then no division is required
Senior Manager
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But, the stem says equal division among 3 people!
What does it mean here?

twixt wrote:
My opinion is not as strutured as yours !

The way I consider this distinct/non distinct stuff is for instance :

X items into 3 groups : non distincts then divide by 3!
X items into 3 groups named A B and C : distinct then no division is required

_________________

Awaiting response,

Thnx & Rgds,
Chandra

Director
Joined: 31 Aug 2004
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IMO just that there are 4 things allocated to each people.
Manager
Joined: 06 Sep 2004
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12C4 * 8C4 * 3! should be the answer.

In factorial form: (12! * 3!)/(4! * 4! * 4!)
Senior Manager
Joined: 22 Jun 2004
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I donot think so. IMO 12C4 * 8C4 * 4C4 is correct.

ssumitsh wrote:
12C4 * 8C4 * 3! should be the answer.

In factorial form: (12! * 3!)/(4! * 4! * 4!)

_________________

Awaiting response,

Thnx & Rgds,
Chandra

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