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

Question

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

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

KanishkM · Answer

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

eabhgoy · Answer

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?

KanishkM · Answer

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.

eabhgoy · Answer

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?

KanishkM · Answer

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

ScottTargetTestPrep · Answer

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:

/

4/11

Answer: B

energetics · Answer

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.

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