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

Question

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?

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

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

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

kunalcvrce · Accepted Answer

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

GMATBusters · Answer

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
Answer E

@s · Answer

Hi Gmatbusters

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

beesh1 · Answer

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.

EgmatQuantExpert · Answer

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.
 
 Answer: E

Rishi91 · Answer

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

EgmatQuantExpert · Answer

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

@s · Answer

Hi

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

Thanks

chetan2u · Answer

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

JeffTargetTestPrep · Answer

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.

Answer: E

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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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