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# 6 people form groups of 2 for a practical work. Each group

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16 Sep 2012, 09:02
fameatop wrote:
Bunuel wrote:
Gusano97 wrote:
A) 6 people form groups of 2 for a practical work. Each group is assigned one of three continents: Asia, Europe or Africa. In how many different ways can the work be organized?

B) In a group of 10 people, 6 women and 4 men. If a comission of three people has to be formed with at least one man, how many groups can we form?

Hi, and welcome to the Gmat Club. Below are the solutions for your problems. Hope it helps.

A. 6 people form groups of 2 for a practical work. Each group is assigned one of three continents: Asia, Europe or Africa. In how many different ways can the work be organized?

# of ways 6 people can be divided into 3 groups when order matters is: $$C^2_6*C^2_4*C^2_2=90$$.

Hi Bunuel,

In reference to the first question, i have a doubt which is- 90 is the no of ways in which 6 people can be divided into 3 groups of 2 persons each.
Shouldn't the answer be 90 x 6 = 540 because these 3 different teams can be sent to 3 different location in 3! ways.

Kindly correct me if i am wrong.

You are right, it should be 90*3! = 540. Order of groups matters here, as we have different continents.
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Re: 6 people form groups of 2 for a practical work. Each group [#permalink]

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28 Dec 2012, 03:35
Gusano97 wrote:
A) 6 people form groups of 2 for a practical work. Each group is assigned one of three continents: Asia, Europe or Africa. In how many different ways can the work be organized?

My approach:
How many ways to select 2-2-2 from 6 people?
$$=\frac{6!}{2!4!}*\frac{4!}{2!2!}*\frac{2!}{2!} = 90$$

How many ways to distribute to 3 groups? $$\frac{3!}{3!}=1$$
We divided by 3! because of 2 2 2 are identical distributions over 3 groups.

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Re: 6 people form groups of 2 for a practical work. Each group [#permalink]

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28 Dec 2012, 03:39
Gusano97 wrote:
A)
In a group of 10 people, 6 women and 4 men. If a comission of three people has to be formed with at least one man, how many groups can we form?

What are our possibilities:
M M M $$=\frac{4!}{3!1!}=4$$
M W W $$=\frac{4!}{1!3!}*\frac{6!}{2!4!}= 4 * 15 = 60$$
M M W $$=\frac{4!}{2!2!}*\frac{6!}{1!5!} = 6 * 6 = 36$$

$$=60+4+36 = 100$$

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22 Jan 2014, 16:19
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02 Apr 2015, 14:30
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Re: 6 people form groups of 2 for a practical work. Each group   [#permalink] 02 Apr 2015, 14:30

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