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# A committee needs to be formed of 3 women and 2 men from a group of 6

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e-GMAT Representative
Joined: 04 Jan 2015
Posts: 2466
A committee needs to be formed of 3 women and 2 men from a group of 6  [#permalink]

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Updated on: 13 Aug 2018, 06:45
00:00

Difficulty:

65% (hard)

Question Stats:

58% (02:15) correct 42% (02:30) wrong based on 166 sessions

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Learn when to “Add” and “Multiply” in Permutation & Combination questions- Exercise Question #3

A committee needs to be formed of 3 women and 2 men from a group of 6 women and 5 men. Among the chosen members, one needs to be selected for the post of the President, and one for the post of Secretary. In how many ways can the President and Secretary be chosen from this committee formed?

Options:
A) 200
B) 400
C) 600
D) 800
E) 4000

Learn to use the Keyword Approach in Solving PnC question from the following article:

Learn when to “Add” and “Multiply” in Permutation & Combination questions

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Originally posted by EgmatQuantExpert on 04 Apr 2018, 05:45.
Last edited by EgmatQuantExpert on 13 Aug 2018, 06:45, edited 6 times in total.
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Re: A committee needs to be formed of 3 women and 2 men from a group of 6  [#permalink]

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04 Apr 2018, 06:21
1
2
EgmatQuantExpert wrote:

Question:

A committee needs to be formed of 3 women and 2 men from a group of 6 women and 5 men. Among the chosen members, one needs to be selected for the post of the President, and one for the post of Secretary. In how many ways can the President and Secretary be chosen from this committee formed?

Options:
A) 200
B) 400
C) 600
D) 800
E) 4000

From grp of 6 women and 5 men , 3 women and 2 men can be selected in 6C3*5C2.
among total selected 5, 5C1 ways for president and 4C1 ways for Secretary .
so total ways=6C3*5C2*5C1*4C1 =4000

option E

Total ways=6C3*5C2*5C1*4C1 =4000

option E
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Re: A committee needs to be formed of 3 women and 2 men from a group of 6  [#permalink]

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04 Apr 2018, 06:34
1
We need to form the group first
From group of 6 women and 5 men , 3 women and 2 men can be selected in 6C3*5C2.= 20*10=200
among total selected 5, we need to select 2 persons- 1 for president , 1 for Secretary = selection and ordering of 2 persons= 5C2*2! =20
so total ways=200*20 =4000
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Joined: 12 Sep 2017
Posts: 28
Re: A committee needs to be formed of 3 women and 2 men from a group of 6  [#permalink]

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08 Apr 2018, 02:09
gmatbusters wrote:
We need to form the group first
From group of 6 women and 5 men , 3 women and 2 men can be selected in 6C3*5C2.= 20*10=200
among total selected 5, we need to select 2 persons- 1 for president , 1 for Secretary = selection and ordering of 2 persons= 5C2*2! =20
so total ways=200*20 =4000

Hi Gmatbusters

Can you please tell why the ordering is important in selection of president and secretary?
Intern
Joined: 19 Oct 2017
Posts: 4
Re: A committee needs to be formed of 3 women and 2 men from a group of 6  [#permalink]

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08 Apr 2018, 16:21
1
@s wrote:
gmatbusters wrote:
We need to form the group first
From group of 6 women and 5 men , 3 women and 2 men can be selected in 6C3*5C2.= 20*10=200
among total selected 5, we need to select 2 persons- 1 for president , 1 for Secretary = selection and ordering of 2 persons= 5C2*2! =20
so total ways=200*20 =4000

Hi Gmatbusters

Can you please tell why the ordering is important in selection of president and secretary?

Lets say we pick person A and person B.
Once person A is picked for president, A cannot be picked again for secretary.
We must select person B. Thus ordering is important. If something has already been picked/used and it cannot be picked again, I consider order to be important.
e-GMAT Representative
Joined: 04 Jan 2015
Posts: 2466
Re: A committee needs to be formed of 3 women and 2 men from a group of 6  [#permalink]

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08 Apr 2018, 20:38

Solution:

Given:
• The committee needs to have 5 members- 3 women and 2 men from 6 women and 5 men.

To find:
• We need to find the number of ways in which 1 president and 1 secretary can be selected from the committee of 5 members.

Approach and Working:

We have to select 1 member for the post of president and 1 member for the post of secretary from the committee formed.
But first, we need to select the 5 members of the committee from 6 women and 5 men.

We can see both the events are dependent on each other, hence, we will apply AND or multiplication to find the total ways.
• Thus, total ways to select the president and the secretary= Ways to form the committee* Ways to select 1 president and 1 secretary from 5 members of the committee

Ways to form the committee:
• Total ways= Ways to select 2 men from 5 men and ways to select 3 women from 6 women
• Total Ways= 5c2*6c3= 10*20=200

Ways to select 1 president and 1 secretary:

If 1 person is president, he cannot be secretary. Thus, both the events are dependent on each other.
Hence, we will multiply the cases.
• Total ways= Ways to select 1 president from 5 members AND ways to select 1 secretary from remaining members
• Total ways= 5*4=20
Hence, total ways to select the president and secretary= 200*20= 4000

Hence, the correct answer is option E.

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Re: A committee needs to be formed of 3 women and 2 men from a group of 6  [#permalink]

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14 Apr 2018, 20:42
Hi

I would be happy to clear the doubt!!!

Let us assume Case 1: A becomes President , B becomes Secretary & Case 2: B becomes President , A becomes Secretary.
Since these two is different case possible , hence ordering is important.

While in case of making groups only : Case : A, B are in the group . Case : B, A are in the group.
These two are not different cases, both are the same. hence ordering is not important here.
.

Please let me know that it u haven't understood it yet.

in pursuit of kudos

@s wrote:
gmatbusters wrote:
We need to form the group first
From group of 6 women and 5 men , 3 women and 2 men can be selected in 6C3*5C2.= 20*10=200
among total selected 5, we need to select 2 persons- 1 for president , 1 for Secretary = selection and ordering of 2 persons= 5C2*2! =20
so total ways=200*20 =4000

Hi Gmatbusters

Can you please tell why the ordering is important in selection of president and secretary?
e-GMAT Representative
Joined: 04 Jan 2015
Posts: 2466
Re: A committee needs to be formed of 3 women and 2 men from a group of 6  [#permalink]

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17 Apr 2018, 06:38
@s wrote:
gmatbusters wrote:
We need to form the group first
From group of 6 women and 5 men , 3 women and 2 men can be selected in 6C3*5C2.= 20*10=200
among total selected 5, we need to select 2 persons- 1 for president , 1 for Secretary = selection and ordering of 2 persons= 5C2*2! =20
so total ways=200*20 =4000

Hi Gmatbusters

Can you please tell why the ordering is important in selection of president and secretary?

Hey,

We have explained a similar question in the article:Fool-proof method to Differentiate between Permutation & Combination Questions

Please go through the article and let me know in case of any doubts

Regards,
Ashutosh
e-GMAT
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Intern
Joined: 12 Sep 2017
Posts: 28
Re: A committee needs to be formed of 3 women and 2 men from a group of 6  [#permalink]

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13 Jun 2018, 02:40
gmatbusters wrote:
We need to form the group first
From group of 6 women and 5 men , 3 women and 2 men can be selected in 6C3*5C2.= 20*10=200
among total selected 5, we need to select 2 persons- 1 for president , 1 for Secretary = selection and ordering of 2 persons= 5C2*2! =20
so total ways=200*20 =4000

Hi

<among total selected 5, we need to select 2 persons- 1 for president , 1 for Secretary = selection and ordering of 2 persons= 5C2*2! =20>

In the above calculaltion, why is it different when i do 200* 5C1 * 4C1 * 2! = 8000

Thanks
Math Expert
Joined: 02 Aug 2009
Posts: 7213
Re: A committee needs to be formed of 3 women and 2 men from a group of 6  [#permalink]

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13 Jun 2018, 02:51
@s wrote:
gmatbusters wrote:
We need to form the group first
From group of 6 women and 5 men , 3 women and 2 men can be selected in 6C3*5C2.= 20*10=200
among total selected 5, we need to select 2 persons- 1 for president , 1 for Secretary = selection and ordering of 2 persons= 5C2*2! =20
so total ways=200*20 =4000

Hi

<among total selected 5, we need to select 2 persons- 1 for president , 1 for Secretary = selection and ordering of 2 persons= 5C2*2! =20>

In the above calculaltion, why is it different when i do 200* 5C1 * 4C1 * 2! = 8000

Thanks

When you use 5c1*4c1, you are already taking order in account, so you don't require to multiply by 2!..
For president you chose 1 in 5 ways, so the secretary can be from remaining 4 ways = 5*4 which is nothing but 5c1*4c1
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Re: A committee needs to be formed of 3 women and 2 men from a group of 6  [#permalink]

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16 Jun 2018, 09:06
Quote:

A committee needs to be formed of 3 women and 2 men from a group of 6 women and 5 men. Among the chosen members, one needs to be selected for the post of the President, and one for the post of Secretary. In how many ways can the President and Secretary be chosen from this committee formed?

A) 200
B) 400
C) 600
D) 800
E) 4000

The number of ways to select three women is 6C3 = (6 x 5 x 4)/3! = 20.

The number of ways to select 2 men is 5C2 = (5 x 4)/2! = 10.

The number of ways to select a president and secretary is 5P2 = 5 x 4 = 20

So the total number of ways is 20 x 10 x 20 = 4000.

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Re: A committee needs to be formed of 3 women and 2 men from a group of 6 &nbs [#permalink] 16 Jun 2018, 09:06
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