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

AAPL wrote:GMAT Prep

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?

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

OA C

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

AAPL wrote:GMAT Prep

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

OA C

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)]

= 16/5

Answer: C