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In a certain group of 10 members, 4 members teach only French and the

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In a certain group of 10 members, 4 members teach only French and the  [#permalink]

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New post Updated on: 03 Sep 2014, 11:58
10
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

79% (02:03) correct 21% (02:07) wrong based on 326 sessions

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In a certain group of 10 members, 4 members teach only French and the rest teach only Spanish or German. If the group is to choose 3-member committee, which must have at least 1 member who teaches French, how many different committee can be chosen ?

A. 40
B. 50
C. 64
D. 80
E. 100

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Originally posted by jet1445 on 26 Feb 2007, 11:08.
Last edited by Bunuel on 03 Sep 2014, 11:58, edited 1 time in total.
Renamed the topic, edited the question, added the OA and moved to PS forum.
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Re: In a certain group of 10 members, 4 members teach only French and the  [#permalink]

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New post 26 Feb 2007, 21:05
6
2
Total possible combinations = 10C3=120
No French(only Spanish or German)=6c3=20
Atleast one French=120-20=100
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Re: In a certain group of 10 members, 4 members teach only French and the  [#permalink]

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New post 26 Feb 2007, 20:40
1
jet1445 wrote:
1.In a certain group of 10 members, 4 members teach only French and the rest teach only Spanish or German. If the group is to choose 3-member committee, which must have at least 1 member who teaches French, how many different committee can be chosen ?
A.40
B.50
C.64
D.80
E.100


Case 1

1french 2either German or Spanish: 4C1 * 6C2 = 4 * 15 = 60

Case 2

2french 1either German or Spanish: 4C2 * 6C1 = 6 * 6 = 36

Case 3

3french 4C3 = 4

Answer is E = 100
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Re: In a certain group of 10 members, 4 members teach only French and the  [#permalink]

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New post 19 Dec 2007, 04:55
In a certain group of 10 members, 4 memebers teach only French and the rest teach only Spanish or German. If the group is to choose a 3-member committee, which must have at least 1 member who teaches Frechn, how many different committees can be chosen?

A) 40

B) 50

C) 64

D) 80

E) 100



I know this is simple, but can anyone please explain the way to solve it? And also does anyone of a good interenet resources where one can practice combinatorics/probablity things?
Thank you.
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Re: In a certain group of 10 members, 4 members teach only French and the  [#permalink]

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New post 19 Dec 2007, 05:15
E

N=10C3-6C3=10*9*8/3*2-6*5*4/3*2=100

CaspAreaGuy wrote:
And also does anyone of a good interenet resources where one can practice combinatorics/probablity things?
Thank you.


Use GMATclub forum. You can also take a look at http://www.gmatclub.com/forum/t56486
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Re: In a certain group of 10 members, 4 members teach only French and the  [#permalink]

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New post 19 Dec 2007, 05:22
Thank you for the link, Walker!
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Re: In a certain group of 10 members, 4 members teach only French and the  [#permalink]

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New post 19 Dec 2007, 07:13
[In a certain group of 10 members, 4 memebers teach only French and the rest teach only Spanish or German. If the group is to choose a 3-member committee, which must have at least 1 member who teaches Frechn, how many different committees can be chosen?

A) 40

B) 50

C) 64

D) 80

E) 100



The total number of combinations of three elements is 10c3=120
The total number of combinations of three elements without French is 6c3=20

The difference between the 2 results is 100
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Re: In a certain group of 10 members, 4 members teach only French and the  [#permalink]

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New post 03 Sep 2014, 11:53
'at least' problems is better solved by making [TOTAL] - [NO ONE]
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Re: In a certain group of 10 members, 4 members teach only French and the  [#permalink]

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New post 07 Sep 2016, 17:32
This tutorial helped me a lot in understanding and applying combinatorics concept.

https://www.manhattanprep.com/gmat/tuto ... bility.cfm

Thanks a lot to guys at Manhattan Prep
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Re: In a certain group of 10 members, 4 members teach only French and the  [#permalink]

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New post 15 Oct 2016, 08:39
please correct me if I am right( I am new to this web site)
1. I count all possibilities without restriction: 10!/3!7!=120
2. Count is there is no French members in the committee 6!/3!3!=20
3. 120-20=100
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Re: In a certain group of 10 members, 4 members teach only French and the  [#permalink]

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New post 15 Oct 2016, 08:44
maray wrote:
please correct me if I am right( I am new to this web site)
1. I count all possibilities without restriction: 10!/3!7!=120
2. Count is there is no French members in the committee 6!/3!3!=20
3. 120-20=100


Yes, this is another way to solve this question. I also solved in similar way. :)
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In a certain group of 10 members, 4 members teach only French and the  [#permalink]

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New post 15 Oct 2016, 13:16
We have two categories of teachers : F (French) and O (others, German and Spanish),
and we have to choose a committee of 3 persons, such as there is at least one French teacher.

So 3 possibilities :
FOO
FFO
FFF

1/ 1 from 4 * 2 from 6 = 4 * (6*5/2) = 60

2/ 2 from 4 * 1 from 6 = (4*3/2) * 6 = 36

3/ 3 from 4 = (4*3*2/3*2) = 4

We add the 3 solutions : 60 + 36 + 4 = 100, answer choice E
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Re: In a certain group of 10 members, 4 members teach only French and the  [#permalink]

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Re: In a certain group of 10 members, 4 members teach only French and the &nbs [#permalink] 11 Jul 2018, 04:31
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