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: \(C^2_6*C^2_4*C^2_2=90\).

Answer: 90.

Similar topics:

probability-85993.html?highlight=divide+groupscombination-55369.html#p690842probability-88685.html#p669025combination-groups-and-that-stuff-85707.html#p642634sub-committee-86346.html?highlight=divide+groupsB. 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?Let's find the probability of the opposite event and subtract it from 1.

Opposite event would be that in the committee of 3 won't be any man (so only women) - \(P(m=0)=P(w=3)=\frac{C^3_6}{C^3_{10}}=\frac{1}{6}\). \(C^3_6\) - # of ways to choose 3 women out 6 women; \(C^3_{10}\) - total # of ways to choose 3 people out of 10.

\(P(m\geq{1})=1-P(m=0)=1-\frac{1}{6}=\frac{5}{6}\).

Answer: \(\frac{5}{6}\)

Hi

Bunuel !

With reference to your one previous post mentioned below:

GENERAL RULE:

1. The number of ways in which \(mn\) different items can be divided equally into \(m\) groups, each containing \(n\) objects and the order of the groups is important is \(\frac{(mn)!}{(n!)^m}\)

2. The number of ways in which \(mn\) different items can be divided equally into \(m\) groups, each containing \(n\) objects and the order of the groups is NOT important is \(\frac{(mn)!}{(n!)^m*m!}\).

Why is order important in both these questions? Perhaps I'm not able to get the real rationale behind 'order'.

I presumed the order to be inconsequential and hence divided the equations in both questions by 2 .

Can you please help me in understanding the concept of order.

Specifically can you please tell how relevance of order create distinct groups(if you can actually mention the groups) in the 2nd example:

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? Thanks in advance !

Regards

SR