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The 23 members of a high school debate club will be split up
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20 Dec 2019, 10:35
20 Dec 2019, 10:35
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Question Stats:
73% (01:20) correct
26% (01:37) wrong based on 108 sessions
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The 23 members of a high school debate club will be split up into two groups -- a 7-member traveling team and a 16-member home team. Every person in the debate club will be on either the traveling team or the home team, but not both.
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 |
The total number of different possible traveling teams that could be chosen |
The total number of different possible home teams that could be chosen |
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
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: The 23 members of a high school debate club will be split up
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21 Dec 2019, 06:28
21 Dec 2019, 06:28
3
Carcass wrote:
The 23 members of a high school debate club will be split up into two groups -- a 7-member traveling team and a 16-member home team. Every person in the debate club will be on either the traveling team or the home team, but not both.
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.
Quantity A |
Quantity B |
The total number of different possible traveling teams that could be chosen |
The total number of different possible home teams that could be chosen |
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.
Quantity A: We need to select 7 students (from 23 students) to be on the travelling team. We can accomplish this in 23C7 ways
Quantity B: We need to select 16 students (from 23 students) to be on the home team. We can accomplish this in 23C16 ways
IMPORTANT: Notice that, when it comes to selecting those 16 students, we can accomplish the task in two ways.
Option #1: We can select 16 of the 23 students to be on the home team (= 23C16).
Option #2: We can select 7 of the 23 students to NOT be on the home team, which means the remaining 16 students WILL be on the home team (= 23C7).
Since both options will yield the same result, we can conclude that 23C16 = 23C7
Answer: C
Key combinations property: nCr = nC(n-r)
Some examples:
10C7 = 10C3
8C1 = 8C7
11C6 = 11C5
Cheers,
Brent
Re: The 23 members of a high school debate club will be split up
[#permalink]
25 Dec 2019, 01:47
25 Dec 2019, 01:47
2
So in the first case , you need to choose 7 members for a collection out of 23 members, this can be done in C23,7 ways. On the other hand, you need to choose 16 members out of 23 members, which gives us C23,16 possible combinations. Therefore, reducing the term C23,16 to C23, (23-16) => C23,7. Consequently, the two given quantities are equal.
