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Of the 7 members of the city council, 4 are Democrats and 3
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02 Oct 2019, 05:12
02 Oct 2019, 05:12
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Of the 7 members of the city council, 4 are Democrats and 3 are Republicans. T is the total number of different 3-person committees that can be appointed from the council membership such that each committee consists of 2 Democrats and 1 Republican.
A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
Kudos for the right answer and explanation
Quantity A |
Quantity B |
T |
15 |
A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
Kudos for the right answer and explanation
Re: Of the 7 members of the city council, 4 are Democrats and 3
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02 Oct 2019, 07:49
02 Oct 2019, 07:49
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Answer is A.
This is combination question(selection).
There are 4D and 3R from which we need to select 2D and 1R.
Total combinations(T) = 4C2 * 3C1
Using the formula nCr = n!/r!(n-r)!
T = 24/4 * 3 = 18
This is greater than 15.
This is combination question(selection).
There are 4D and 3R from which we need to select 2D and 1R.
Total combinations(T) = 4C2 * 3C1
Using the formula nCr = n!/r!(n-r)!
T = 24/4 * 3 = 18
This is greater than 15.
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Re: Of the 7 members of the city council, 4 are Democrats and 3
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02 Oct 2019, 09:02
02 Oct 2019, 09:02
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Carcass wrote:
Of the 7 members of the city council, 4 are Democrats and 3 are Republicans. T is the total number of different 3-person committees that can be appointed from the council membership such that each committee consists of 2 Democrats and 1 Republican.
Quantity A |
Quantity B |
T |
15 |
Take the task of creating 3-person committees and break it into stages.
Stage 1: Select 2 Democrats to be on the committee
Since the order in which we select the two Democrats does not matter, we can use combinations.
We can select 2 Democrats from the 4 Democrats in 4C2 ways (6 ways)
So, we can complete stage 1 in 6 ways
Stage 2: Select 1 Republican to be on the committee
There are 3 Republicans to choose from.
So we can complete stage 2 in 3 ways
By the Fundamental Counting Principle (FCP), we can complete the 2 stages (and thus create a 3-person committee) in (6)(3) ways (= 18 ways)
In other words, T = 18
We get:
Quantity A: 18
Quantity B: 15
Answer: A
Note: the FCP can be used to solve the MAJORITY of counting questions on the GRE. So, be sure to learn it.
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