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In how many ways can be 6 boys and 6 girls sit around circular table

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In how many ways can be 6 boys and 6 girls sit around circular table [#permalink]

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New post 22 Jan 2015, 07:52
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In how many ways can be 6 boys and 6 girls sit around circular table so that no two boys sit next to each other?

A. (5!)^2
B. (6!)^2
C. 5!6!
D. 11!
E. (5!)^2*6!

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Spoiler: OA

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Re: In how many ways can be 6 boys and 6 girls sit around circular table [#permalink]

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New post 23 Jan 2015, 10:27
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ANS C..
first fix one boy and place other 5 in alt seats so total ways is 5!
now place each girl between a pair of boys... total ways of seating arrangement of girls 6!
total is 5!*6!
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Re: In how many ways can be 6 boys and 6 girls sit around circular table [#permalink]

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New post 07 Sep 2015, 21:30
Hi Bunuel,

Can we have the OA please. IMO, it should be C.

no.of arrangements for girls= (6-1)!= 5!
This will give 6 empty spaces for 6 boys. Hence, we can arrange them in 6! ways.

c) 5!*6!


Thanks,
Gaurav :-)
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Re: In how many ways can be 6 boys and 6 girls sit around circular table [#permalink]

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New post 07 Sep 2015, 22:10
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No. of ways in which girls can be seated after fixing a seat on the circular table = (6-1)! = 5!
No. of ways in which boys can be seated on the vacant seats = 6!
Total no. of ways = 5!x6!
Answer: C
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Re: In how many ways can be 6 boys and 6 girls sit around circular table [#permalink]

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New post 27 Mar 2017, 23:16
GauravSolanky wrote:
Hi Bunuel,

Can we have the OA please. IMO, it should be C.

no.of arrangements for girls= (6-1)!= 5!
This will give 6 empty spaces for 6 boys. Hence, we can arrange them in 6! ways.

c) 5!*6!


Thanks,
Gaurav :-)


Hi explain a little...
why we are subtracting 1 from girls
TIA
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Re: In how many ways can be 6 boys and 6 girls sit around circular table [#permalink]

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New post 27 Mar 2017, 23:27
ehsan090 wrote:
GauravSolanky wrote:
Hi Bunuel,

Can we have the OA please. IMO, it should be C.

no.of arrangements for girls= (6-1)!= 5!
This will give 6 empty spaces for 6 boys. Hence, we can arrange them in 6! ways.

c) 5!*6!


Thanks,
Gaurav :-)


Hi explain a little...
why we are subtracting 1 from girls
TIA


To find the no.of arrangements in a circular fashion we always use the formula (n-1)! where n is the total number of entities.
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Re: In how many ways can be 6 boys and 6 girls sit around circular table [#permalink]

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New post 27 Mar 2017, 23:47
ehsan090 wrote:
GauravSolanky wrote:
Hi Bunuel,

Can we have the OA please. IMO, it should be C.

no.of arrangements for girls= (6-1)!= 5!
This will give 6 empty spaces for 6 boys. Hence, we can arrange them in 6! ways.

c) 5!*6!


Thanks,
Gaurav :-)


Hi explain a little...
why we are subtracting 1 from girls
TIA


The number of arrangements of n distinct objects in a row is given by \(n!\).
The number of arrangements of n distinct objects in a circle is given by \((n-1)!\).

The difference between placement in a row and that in a circle is following: if we shift all object by one position, we will get different arrangement in a row but the same relative arrangement in a circle. So, for the number of circular arrangements of n objects we have:

\(\frac{n!}{n} = (n-1)!\).

Check other Arrangements in a Row and around a Table questions in our Special Questions Directory.
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Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
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Re: In how many ways can be 6 boys and 6 girls sit around circular table   [#permalink] 27 Mar 2017, 23:47
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