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An organization constructs a committee of 3 people from A, B, C, D, E,

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An organization constructs a committee of 3 people from A, B, C, D, E, [#permalink]

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New post 30 Mar 2018, 02:09
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A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

58% (01:26) correct 42% (00:54) wrong based on 62 sessions

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[GMAT math practice question]

An organization constructs a committee of 3 people from A, B, C, D, E, F and G. A and B are relatives, so they cannot both be committee members at the same time. How many different committees can be formed?

A. 25
B. 30
C. 35
D. 40
E. 45
[Reveal] Spoiler: OA

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An organization constructs a committee of 3 people from A, B, C, D, E, [#permalink]

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New post 30 Mar 2018, 02:26
MathRevolution wrote:
[GMAT math practice question]

An organization constructs a committee of 3 people from A, B, C, D, E, F and G. A and B are relatives, so they cannot both be committee members at the same time. How many different committees can be formed?

A. 25
B. 30
C. 35
D. 40
E. 45


Total number of ways to select three A, B, C, D, E, F and G . total ways to select three--7C3
Another group in which A,B is must then---C, D, E, F and G. total ways to select three--5C1

So total number of ways=7c3-5C1=30.
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Re: An organization constructs a committee of 3 people from A, B, C, D, E, [#permalink]

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New post 30 Mar 2018, 02:43
MathRevolution wrote:
[GMAT math practice question]

An organization constructs a committee of 3 people from A, B, C, D, E, F and G. A and B are relatives, so they cannot both be committee members at the same time. How many different committees can be formed?

A. 25
B. 30
C. 35
D. 40
E. 45


CAN YOU PROVIDE THE EXPLAINATION FOR OPTION B
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Re: An organization constructs a committee of 3 people from A, B, C, D, E, [#permalink]

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New post 30 Mar 2018, 02:54
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teaserbae wrote:
MathRevolution wrote:
[GMAT math practice question]

An organization constructs a committee of 3 people from A, B, C, D, E, F and G. A and B are relatives, so they cannot both be committee members at the same time. How many different committees can be formed?

A. 25
B. 30
C. 35
D. 40
E. 45


CAN YOU PROVIDE THE EXPLAINATION FOR OPTION B


Hi Teaser,

First select three from 7 group of people total ways will be 7C3.
Let consider A and B has been selected then from rest 5 one has to be selected so=5C1.
Both A and B can't be together. So total number of ways in which A and B can't be together will be=Total number of ways-Total ways in which both are together=7C3-5C1.

Hope it will help.
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Re: An organization constructs a committee of 3 people from A, B, C, D, E, [#permalink]

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New post 01 Apr 2018, 18:47
=>
The total number of possible committees of three 3 people chosen from 7 people is 7C3 = 35.
However, we need to exclude the committees containing both A and B.
The number of committees containing A, B and one other person is equal to the number of ways of choosing 1 person from the C, D, E, F, and G, which is 5C1 = 5.
Therefore, the total number of committees 35 – 5 = 30.

Therefore, the answer is B.
Answer: B
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Re: An organization constructs a committee of 3 people from A, B, C, D, E, [#permalink]

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New post 04 Apr 2018, 17:51
MathRevolution wrote:
[GMAT math practice question]

An organization constructs a committee of 3 people from A, B, C, D, E, F and G. A and B are relatives, so they cannot both be committee members at the same time. How many different committees can be formed?

A. 25
B. 30
C. 35
D. 40
E. 45


We can use the formula:

Total number of committees = committees including A and B + committees not including both A and B

Note that since we are choosing 3 people from 7, the total number of committees is:

7C3 = 7!/(4!*3!) = (7*6*5)/(3*2) = 35.

The number of committees including A and B can be found by observing that since A and B already occupy 2 of the 3 available positions, there are 5 choices left for the third person; therefore there are 5 committees including both A and B.

Thus, the number of committees not including both A and B is 35 - 5 = 30.

Answer: B
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Re: An organization constructs a committee of 3 people from A, B, C, D, E,   [#permalink] 04 Apr 2018, 17:51
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