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Ratio of 5-member vs 4-member committees - GMAT prep

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Senior | Next Rank: 100 Posts
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by prata » Mon May 23, 2016 12:21 am
A certain club has 20 members. What is the ratio of 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?

A. 16 to 1
B. 15 to 1
C. 16 to 5
D. 15 to 6
E. 5 to 4
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by OptimusPrep » Tue May 24, 2016 7:04 pm
prata wrote:A certain club has 20 members. What is the ratio of 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?

A. 16 to 1
B. 15 to 1
C. 16 to 5
D. 15 to 6
E. 5 to 4
5 member committee = 20C5
4 member committee = 20C4

Ratio = 20C5 / 20C4 = (20!/15!*5!) * (16!*4!/20!) = 16: 5

Correct option: C
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