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GMATGuruNY
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Good = Total - Bad.ruplun wrote:If among 5 children there are 2 siblings, in how many ways can the children be seated in a row so that the siblings do not sit together?
Total:
Number of ways to arrange the 5 children = 5! = 120.
Bad:
In a bad arrangement, the 2 siblings sit adjacent to each other.
Let [AB] represent the 2 siblings sitting adjacent to each other.
Number of ways to arrange the 4 elements [AB] and the 3 other children = 4! = 24.
Since AB can be reversed to BA, we multiply by 2:
24*2 = 48.
Good = 120-48 = 72.
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Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
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OABAAGMATGuruNY wrote:Good = Total - Bad.ruplun wrote:If among 5 children there are 2 siblings, in how many ways can the children be seated in a row so that the siblings do not sit together?
Total:
Number of ways to arrange the 5 children = 5! = 120.
Bad:
In a bad arrangement, the 2 siblings sit adjacent to each other.
Let [AB] represent the 2 siblings sitting adjacent to each other.
Number of ways to arrange the 4 elements [AB] and the 3 other children = 4! = 24.
Since AB can be reversed to BA, we multiply by 2:
24*2 = 48.
Good = 120-48 = 72.
OAABA
OAAAB
AOABA
AOAAB
AAOAB
BAOAA
BAAOA
ABAOA
BAAAO
ABAAO
AABAO
12 => MULTIPLY BY 2 Total 24.
Why am I wrong?
-
GMATGuruNY
- GMAT Instructor
- Posts: 15539
- Joined: Tue May 25, 2010 12:04 pm
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- Followed by:1906 members
- GMAT Score:790
I'm not sure why you have 3 A's in your arrangements.fr743 wrote:OABAAGMATGuruNY wrote:Good = Total - Bad.ruplun wrote:If among 5 children there are 2 siblings, in how many ways can the children be seated in a row so that the siblings do not sit together?
Total:
Number of ways to arrange the 5 children = 5! = 120.
Bad:
In a bad arrangement, the 2 siblings sit adjacent to each other.
Let [AB] represent the 2 siblings sitting adjacent to each other.
Number of ways to arrange the 4 elements [AB] and the 3 other children = 4! = 24.
Since AB can be reversed to BA, we multiply by 2:
24*2 = 48.
Good = 120-48 = 72.
OAABA
OAAAB
AOABA
AOAAB
AAOAB
BAOAA
BAAOA
ABAOA
BAAAO
ABAAO
AABAO
12 => MULTIPLY BY 2 Total 24.
Why am I wrong?
Call the elements {AB], C, D and E and count all the possible arrangements:
[AB]CDE
[AB]CED
[AB]DCE
[AB]DEC
[AB]ECD
[AB]EDC
There are 6 arrangements in which A occupies position 1 and B occupies position 2.
Since [AB] can be reversed to [BA], we multiply by 2:
Number of of arrangements in which [AB] occupies the first 2 positions = 2*6 = 12.
[AB] can occupy 4 sets of adjacent positions:
Positions 1 and 2
Positions 2 and 3
Positions 3 and 4
Positions 4 and 5
Each set of adjacent positions will yield 12 possible arrangements, as shown above.
Since there are 4 sets of adjacent positions, we multiply by 4:
Total arrangements in which [AB] sit adjacent to each other = 12*4 = 48.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
GMATGuruNY wrote:I'm not sure why you have 3 A's in your arrangements.fr743 wrote:OABAAGMATGuruNY wrote:Good = Total - Bad.ruplun wrote:If among 5 children there are 2 siblings, in how many ways can the children be seated in a row so that the siblings do not sit together?
Total:
Number of ways to arrange the 5 children = 5! = 120.
Bad:
In a bad arrangement, the 2 siblings sit adjacent to each other.
Let [AB] represent the 2 siblings sitting adjacent to each other.
Number of ways to arrange the 4 elements [AB] and the 3 other children = 4! = 24.
Since AB can be reversed to BA, we multiply by 2:
24*2 = 48.
Good = 120-48 = 72.
OAABA
OAAAB
AOABA
AOAAB
AAOAB
BAOAA
BAAOA
ABAOA
BAAAO
ABAAO
AABAO
12 => MULTIPLY BY 2 Total 24.
Why am I wrong?
Call the elements {AB], C, D and E and count all the possible arrangements:
[AB]CDE
[AB]CED
[AB]DCE
[AB]DEC
[AB]ECD
[AB]EDC
There are 6 arrangements in which A occupies position 1 and B occupies position 2.
Since [AB] can be reversed to [BA], we multiply by 2:
Number of of arrangements in which [AB] occupies the first 2 positions = 2*6 = 12.
[AB] can occupy 4 sets of adjacent positions:
Positions 1 and 2
Positions 2 and 3
Positions 3 and 4
Positions 4 and 5
Each set of adjacent positions will yield 12 possible arrangements, as shown above.
Since there are 4 sets of adjacent positions, we multiply by 4:
Total arrangements in which [AB] sit adjacent to each other = 12*4 = 48.
But they must not sit TOGETHER.
-
GMATGuruNY
- GMAT Instructor
- Posts: 15539
- Joined: Tue May 25, 2010 12:04 pm
- Location: New York, NY
- Thanked: 13060 times
- Followed by:1906 members
- GMAT Score:790
Correct.fr743 wrote:GMATGuruNY wrote:I'm not sure why you have 3 A's in your arrangements.fr743 wrote:OABAAGMATGuruNY wrote:Good = Total - Bad.ruplun wrote:If among 5 children there are 2 siblings, in how many ways can the children be seated in a row so that the siblings do not sit together?
Total:
Number of ways to arrange the 5 children = 5! = 120.
Bad:
In a bad arrangement, the 2 siblings sit adjacent to each other.
Let [AB] represent the 2 siblings sitting adjacent to each other.
Number of ways to arrange the 4 elements [AB] and the 3 other children = 4! = 24.
Since AB can be reversed to BA, we multiply by 2:
24*2 = 48.
Good = 120-48 = 72.
OAABA
OAAAB
AOABA
AOAAB
AAOAB
BAOAA
BAAOA
ABAOA
BAAAO
ABAAO
AABAO
12 => MULTIPLY BY 2 Total 24.
Why am I wrong?
Call the elements {AB], C, D and E and count all the possible arrangements:
[AB]CDE
[AB]CED
[AB]DCE
[AB]DEC
[AB]ECD
[AB]EDC
There are 6 arrangements in which A occupies position 1 and B occupies position 2.
Since [AB] can be reversed to [BA], we multiply by 2:
Number of of arrangements in which [AB] occupies the first 2 positions = 2*6 = 12.
[AB] can occupy 4 sets of adjacent positions:
Positions 1 and 2
Positions 2 and 3
Positions 3 and 4
Positions 4 and 5
Each set of adjacent positions will yield 12 possible arrangements, as shown above.
Since there are 4 sets of adjacent positions, we multiply by 4:
Total arrangements in which [AB] sit adjacent to each other = 12*4 = 48.
But they must not sit TOGETHER.
As just shown, there are 48 arrangements in which A and B are next to each other.
These are the bad arrangements.
The total number of ways to arrange the 5 children = 5! = 120.
This is the total number of arrangements.
Thus, of these 120 arrangements, the number of arrangements in which A and B are NOT next to each other = 120-48 = 72.
Total-Bad = Good.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
