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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.
hey I got the correct answer but was just wondering why the members have to be different, i.e. why we are using combinations ?
Re: A certain club has 20 members. What is the ratio of the memb
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28 Feb 2019, 07:08
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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
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
Re: A certain club has 20 members. What is the ratio of the memb
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04 Mar 2019, 20:18
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
The ratio is the following:
(20C5)/(20C4) = [(20 x 19 x 18 x 17 x 16)/5!]/[(20 x 19 x 18 x 17)/4!]
= [(20 x 19 x 18 x 17 x 16)/5!] x [4!/(20 x 19 x 18 x 17)]