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

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A certain club has 20 members. What is the ratio of the memb [#permalink]  25 Mar 2009, 22:04
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71% (01:56) correct 29% (01:11) wrong based on 186 sessions
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
[Reveal] Spoiler: OA
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Re: Permutaion + Combination [#permalink]  25 Mar 2009, 22:17
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C.
20C5/20C4 = 16/5
milind1979 wrote:
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
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Re: Permutaion + Combination [#permalink]  24 Apr 2010, 08:38
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?
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Re: Permutaion + Combination [#permalink]  24 Apr 2010, 08:47
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bakfed wrote:
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?

20C5 = FACT[20] / FACT[5]*FACT[15]
20C4 = FACT[20] / FACT[4]*FACT[16]

20C5 / 20C4 = 16/5
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Re: Permutaion + Combination [#permalink]  24 Apr 2010, 09:05
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bakfed wrote:
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?

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

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.
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Re: Permutaion + Combination [#permalink]  24 Apr 2010, 09:11
bakfed wrote:
brinng back an old post.

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

20*19*18*17*16 is giving all possible ways of selecting 5 people. It also includes the order of a particular selection into account. In this case it does not mater if you select a member first ,second or third as long as it is selected in the group. Therefore, the 20*19*18*17*16 number has repetition of the same group in 5 ways and you have to divide by FACT[5]. Similarly for (20*19*18*17) by FACT[4]
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Re: Permutaion + Combination [#permalink]  19 Dec 2010, 14:46
I initially got this wrong, but see that this is just 20!/15!5! *16!4!/20! the 20! cancels out and you have 16!4!/15!5! which leaves 16/5.
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Re: Permutaion + Combination [#permalink]  29 Aug 2013, 10:11
Bunuel wrote:
bakfed wrote:
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?

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

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.

when should we use 20*19*18*17*16 way and when the second way?
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Re: Permutaion + Combination [#permalink]  31 Aug 2013, 05:38
Expert's post
swati007 wrote:
Bunuel wrote:
bakfed wrote:
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?

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

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.

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

The first case is applicable when the order matters, when, for example, we have member #1, member #2, ...
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A certain club has 20 members. What is the ratio of the [#permalink]  30 Nov 2013, 13:41
A certain club has 20 members. What is the ratio of the number 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?

16 to 1
15 to 1
16 to 5
15 to 6
5 to 4

[Reveal] Spoiler:
PLS explain the OA
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Re: A certain club has 20 members. What is the ratio of the [#permalink]  01 Dec 2013, 05:25
Expert's post
MDK wrote:
A certain club has 20 members. What is the ratio of the number 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?

16 to 1
15 to 1
16 to 5
15 to 6
5 to 4

[Reveal] Spoiler:
PLS explain the OA

Merging similar topics. Please refer tot he solutions above.
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Re: A certain club has 20 members. What is the ratio of the memb [#permalink]  16 Feb 2015, 20:51
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Re: A certain club has 20 members. What is the ratio of the memb   [#permalink] 16 Feb 2015, 20:51
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