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Virat is one among the 15 members of a certain club.

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Virat is one among the 15 members of a certain club.  [#permalink]

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New post 31 Jan 2019, 08:22
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Question Stats:

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Virat is one among the 15 members of a certain club. What is the ratio of the 4-member committees that can be formed from the members of the club including Virat to the number of 4-member committees that can be formed from the members of the club excluding Virat?

A. 3 to 2
B. 4 to 11
C. 1 to 10
D. 4 to 5
E. 1 to 15

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Re: Virat is one among the 15 members of a certain club.  [#permalink]

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New post 31 Jan 2019, 09:45
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eabhgoy wrote:
Virat is one among the 15 members of a certain club. What is the ratio of the 4-member committees that can be formed from the members of the club including Virat to the number of 4-member committees that can be formed from the members of the club excluding Virat?

A. 3 to 2
B. 4 to 11
C. 1 to 10
D. 4 to 5
E. 1 to 15


Ratio of the 4-member committees that can be formed from the members of the club including Virat to the number of 4-member committees that can be formed from the members of the club excluding Virat

No of ways when Virat is include = 1 * 14C3

No of ways when Virat is not includes = 14C4

Ratio = 14C3/ 14C4

B
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Re: Virat is one among the 15 members of a certain club.  [#permalink]

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New post 01 Feb 2019, 02:50
KanishkM wrote:
eabhgoy wrote:
Virat is one among the 15 members of a certain club. What is the ratio of the 4-member committees that can be formed from the members of the club including Virat to the number of 4-member committees that can be formed from the members of the club excluding Virat?

A. 3 to 2
B. 4 to 11
C. 1 to 10
D. 4 to 5
E. 1 to 15


Ratio of the 4-member committees that can be formed from the members of the club including Virat to the number of 4-member committees that can be formed from the members of the club excluding Virat

No of ways when Virat is include = 1 * 14C3

No of ways when Virat is not includes = 14C4

Ratio = 14C3/ 14C4

B


Hey, could you tell me why we used combinations are not simply do: (1*14*13*12*11)/(14*13*12*11*10) = 1 to 10?
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Re: Virat is one among the 15 members of a certain club.  [#permalink]

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New post 01 Feb 2019, 02:58
eabhgoy wrote:
KanishkM wrote:
eabhgoy wrote:
Virat is one among the 15 members of a certain club. What is the ratio of the 4-member committees that can be formed from the members of the club including Virat to the number of 4-member committees that can be formed from the members of the club excluding Virat?

A. 3 to 2
B. 4 to 11
C. 1 to 10
D. 4 to 5
E. 1 to 15


Ratio of the 4-member committees that can be formed from the members of the club including Virat to the number of 4-member committees that can be formed from the members of the club excluding Virat

No of ways when Virat is include = 1 * 14C3

No of ways when Virat is not includes = 14C4

Ratio = 14C3/ 14C4

B


Hey, could you tell me why we used combinations are not simply do: (1*14*13*12*11)/(14*13*12*11*10) = 1 to 10?


Hi eabhgoy

IMO, what you have done is filled 5 places, even if we take 4 places ( we will get the ratio as 1 to 11) we wont be sure in how many ways the remaining players will occupy the remaining places, that's why we took a combinations approach rather than a dash approach.
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If you notice any discrepancy in my reasoning, please let me know. Lets improve together.

Quote which i can relate to.
Many of life's failures happen with people who do not realize how close they were to success when they gave up.

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Joined: 12 Apr 2011
Posts: 47
Location: United Arab Emirates
Concentration: Strategy, Marketing
Schools: CBS '21, Yale '21, INSEAD
GMAT 1: 670 Q50 V31
WE: Marketing (Telecommunications)
Re: Virat is one among the 15 members of a certain club.  [#permalink]

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New post 01 Feb 2019, 03:05
KanishkM wrote:
eabhgoy wrote:
KanishkM wrote:

Ratio of the 4-member committees that can be formed from the members of the club including Virat to the number of 4-member committees that can be formed from the members of the club excluding Virat

No of ways when Virat is include = 1 * 14C3

No of ways when Virat is not includes = 14C4

Ratio = 14C3/ 14C4

B


Hey, could you tell me why we used combinations are not simply do: (1*14*13*12*11)/(14*13*12*11*10) = 1 to 10?


Hi eabhgoy

IMO, what you have done is filled 5 places, even if we take 4 places ( we will get the ratio as 1 to 11) we wont be sure in how many ways the remaining players will occupy the remaining places, that's why we took a combinations approach rather than a dash approach.


Thanks, buddy...yes I meant to show for 4 people which makes the ratio 1:11.

Apologies for asking really basic questions but what do u mean when u say "how many ways the remaining players will occupy the remaining places"?

I guess what I am asking is when to use the dash approach vs combinations?
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Re: Virat is one among the 15 members of a certain club.  [#permalink]

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New post 01 Feb 2019, 03:14
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eabhgoy wrote:

Thanks, buddy...yes I meant to show for 4 people which makes the ratio 1:11.

Apologies for asking really basic questions but what do u mean when u say "how many ways the remaining players will occupy the remaining places"?

I guess what I am asking is when to use the dash approach vs combinations?


eabhgoy

No worries.

But your next question did stump me :). I wont have a very clear answer for this.

IMO it varies from case to case. Like if i had to select 3 numbers from a set of 4 numbers i would had used dash approach.

But if you still have that doubt, kindly look into the topic mega thread of Combinations. Your answer should be there :)
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Re: Virat is one among the 15 members of a certain club.  [#permalink]

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New post 04 Feb 2019, 17:40
eabhgoy wrote:
Virat is one among the 15 members of a certain club. What is the ratio of the 4-member committees that can be formed from the members of the club including Virat to the number of 4-member committees that can be formed from the members of the club excluding Virat?

A. 3 to 2
B. 4 to 11
C. 1 to 10
D. 4 to 5
E. 1 to 15


The number of 4-member committees that can be created with Virat is:

14C3 x 1C1 = 14C3

and the number without Virat is:

14C4 x 1C0 = 14C4

Therefore, the ratio is:

[(14 x 13 x 12)/(3 x 2)]/[(14 x 13 x 12 x 11)/(4 x 3 x 2)]

[(14 x 13 x 12)(4 x 3 x 2)]/[(14 x 13 x 12 x 11)(3 x 2)]

4/11

Answer: B
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Virat is one among the 15 members of a certain club.  [#permalink]

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New post 13 Feb 2019, 13:35
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numerator: V 1* Others 14*13*12 *4 (V's place)
denom: Others, not V = 14*13*12*11
Cancels out to 4/11.

The reason we multiply by 4 in the numerator is we have to account for Virat's place, since he is unique and other people are interchangeable, he can be put in any of the 4 slots, too. So we have 1 choice for virat but 4 slots.
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Virat is one among the 15 members of a certain club.   [#permalink] 13 Feb 2019, 13:35
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