A certain club has 20 members. What is the ratio of the number of

Question

A certain club has 20 members. What is the ratio of the member of 5-member
committees that can be formed from the members of the club to the number of 4-member
committees that can be formed from the members of the club?
A. 16 to 1
B. 15 to 1
C. 16 to 5
D. 15 to 6
E. 5 to 4

A. 16 to 1
B. 15 to 1
C. 16 to 5
D. 15 to 6
E. 5 to 4

Bunuel · Accepted Answer

\frac{C^5_{20}}{C^4_{20}}=\frac{20!}{15!*5!}*\frac{16!*4!}{20!}=\frac{16}{5}

Second question:

20*19*18*17*16 does not give you # of 5 member committees out of 20. You need to divide this by 5! to get rid of the repetitions (factorial correction). The same for 20*19*18*17, you should divide this by 4!.

Take another example: how many committees of 2 can be formed out of A, B and C?

AB
AC
BC
Only 3, which is  C^2_3=3 .

But the way you are doing you'd get 3*2=6. This number has repetitions so we should divide it by 2! --> 6/2!=3.

Hope it's clear.

Economist · Answer

C.
20C5/20C4 = 16/5

bakfed · Answer

brinng back an old post.

I somehow can't get 20C5/20C4 to be 16/5; I keep on getting 8/5

Also, for this question, why can't we just do the following:
(20*19*18*17*16)/(20*19*18*17) = 16/1?

msand · Answer

20C5 = FACT  / FACT *FACT 
20C4 = FACT  / FACT *FACT

20C5 / 20C4 = 16/5

swati007 · Answer

when should we use 20*19*18*17*16 way and when the second way?

Bunuel · Answer

The first case is applicable when the order matters, when, for example, we have member #1, member #2, ...

honchos · Answer

Isnt the Question doubtful?

They didnt mentioned that first we have to select 5 members then 4 from the remaining 15?

ENGRTOMBA2018 · Answer

That is exactly the reason why you need to treat "selecting 5 out of 20" and "selecting 4 out of 20" as 2 independent events. Per the question, there is no overlap in the 2 cases.

Thus the final answer = 20C5 / 20C4 = 16/5

GMATinsight · Answer

The question is absolutely clear and holds no ambiguity in the language

Question : A certain club has 20 members. What is the ratio of the member of 5-member committees that can be formed from the members of the club to the number of 4-member committees that can be formed from the members of the club?"

The two actions (making the committee of 5 members AND making the committee of 4 embers) are to be treated independently.

No. of Ways to make 5 member committee out of 20 members = 20C5 = 15504

No. of Ways to make 4 member committee out of 20 members = 20C4 = 4845

Required ratio = 15504 / 4845 = 16/5

honchos · Answer

Thanks, My doubt is still the same. They didn't mentioned that two events are mutually independent or dependent. 
This is a very easy question, but I was spinned that how should I interpret the language - Mutually independent or independent.

GMATinsight · Answer

The question did NOT mentioned that  "Team of 4 has to be selected out of the REMAINING"

If the word "remaining" has not been used then it is Independent event case.

I hope it helps1

HarveyKlaus · Answer

Hello guys,

Can I please ask how 20C5 / 20C4 has been solved to get the fraction 16/5?
I know that one way to solve this is by doing the long multiplication thing but Brunnel has calculated it in a simplified manner. Can someone please write down the steps?

Thanks,

GMATinsight · Answer

20C5 = 20!/  = 20*19*18*17*16/5! = 19*3*17*16

20C4 = 20!/  = 20*19*18*17/4! = 5*19*3*17

20C5 / 20C4 = 19*3*17*16 / 5*19*3*17 = 16/5

I hope this helps!!!

BrentGMATPrepNow · Answer

5-member committees  
Since the order in which we select the committee members does not matter, we can use COMBINATIONS
We can select 5 people from 20 people in 20C5 ways
20C5 =  (20)(19)(18)(17)(16)/(5)(4)(3)(2)(1)

4-member committees  
Since the order in which we select the committee members does not matter, we can use COMBINATIONS
We can select 4 people from 20 people in 20C4 ways
20C4 =  (20)(19)(18)(17)/(4)(3)(2)(1)

The RATIO =  (20)(19)(18)(17)(16)/(5)(4)(3)(2)(1) ]/ (20)(19)(18)(17)/(4)(3)(2)(1) ]
=  (20)(19)(18)(17)(16)/(5)(4)(3)(2)(1) ] (4)(3)(2)(1)/(20)(19)(18)(17) ]
=(20)(19)(18)(17)(16)(4)(3)(2)(1)/(20)(19)(18)(17)(5)(4)(3)(2)(1)
= (20)(19)(18)(17) (16) (4)(3)(2)(1) / (20)(19)(18)(17) (5) (4)(3)(2)(1) 
=16/5

Answer: C

Cheers, 
Brent

RELATED VIDEO
 https://www.youtube.com/watch?v=05a0A7vjG8I

ScottTargetTestPrep · Answer

The ratio is the following:

(20C5)/(20C4) =  /

=   x

= 16/5

Answer: C

bumpbot · Answer

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A certain club has 20 members. What is the ratio of the number of

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