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

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Director
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In how many ways 12 different things can be divided equally [#permalink]

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12 Jan 2005, 18:30
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In how many ways 12 different things can be divided equally among 3 people.

The answer is in Factorial form.
VP
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12 Jan 2005, 21:44
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
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Re: PS: Another counting problem [#permalink]

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13 Jan 2005, 01:05

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.

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Awaiting response,

Thnx & Rgds,
Chandra

Director
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13 Jan 2005, 06:20
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
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13 Jan 2005, 08:39
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
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13 Jan 2005, 08:44
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 ?

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Awaiting response,

Thnx & Rgds,
Chandra

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13 Jan 2005, 08:52
Hi Malellac,

My vision was the opposite as people here are not distinct...
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13 Jan 2005, 08:58
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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13 Jan 2005, 09:14
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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13 Jan 2005, 09:18
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

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Thnx & Rgds,
Chandra

Director
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13 Jan 2005, 09:21
IMO just that there are 4 things allocated to each people.
Manager
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13 Jan 2005, 15:22
12C4 * 8C4 * 3! should be the answer.

In factorial form: (12! * 3!)/(4! * 4! * 4!)
Senior Manager
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13 Jan 2005, 23:57
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!)

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Awaiting response,

Thnx & Rgds,
Chandra

13 Jan 2005, 23:57
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