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How many ways are there for 3 males and 3 females to sit

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zisis
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How many ways are there for 3 males and 3 females to sit [#permalink] New post   18 Dec 2010, 05:18
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How many ways are there for 3 males and 3 females to sit (around a circular table) if no male should sit next to a male (and no female next to female) and Mary wants to sit with her back on the wall?

A. 6
B. 12
C. 72
D. 100
E. 720
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Bunuel
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Re: Circular table [#permalink] New post   18 Dec 2010, 06:22
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zisis wrote:
How many ways are there for 3 males and 3 females to sit if no male should sit next to a male (and no female next to female) and Mary wants to sit with her back on the wall?

6
12
72
100
720


I guess they sit around the table as you mention it in the title of the topic.

So Mary has her own chair, fixed position. Other two females around the table can sit in 2 ways: the first to the left of Mary and the second to the right or vise-versa. Now, if 3 males will sit between them then no two female or two male will sit next to each other (female-male-female-male-female-male). But these males on their spots can also sit in different ways, namely in 3! different ways, so total 2*3!=12.

Answer B.
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honchos
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Re: Circular table [#permalink] New post   20 Sep 2013, 01:34
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Bunuel wrote:
zisis wrote:
How many ways are there for 3 males and 3 females to sit if no male should sit next to a male (and no female next to female) and Mary wants to sit with her back on the wall?

6
12
72
100
720


I guess they sit around the table as you mention it in the title of the topic.

So Mary has her own chair, fixed position. Other two females around the table can sit in 2 ways: the first to the left of Mary and the second to the right or vise-versa. Now, if 3 males will sit between them then no two female or two male will sit next to each other (female-male-female-male-female-male). But these males on their spots can also sit in different ways, namely in 3! different ways, so total 2*3!=12.

Answer B.


Lets first sit the 3 man, 2! ways.

Now since one position is fixed for women, there are 2 women left and they have 2! ways

2! X 2! = 4 answer is diff this way.

or shall we give possibility of 3 ways for women to be fixed with back facing so 3! ways, Lets discuss the doubt.

If u like my way of discussion plz give Kudos.
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Bunuel
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Re: Circular table [#permalink] New post   20 Sep 2013, 01:43
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honchos wrote:
Bunuel wrote:
zisis wrote:
How many ways are there for 3 males and 3 females to sit if no male should sit next to a male (and no female next to female) and Mary wants to sit with her back on the wall?

6
12
72
100
720


I guess they sit around the table as you mention it in the title of the topic.

So Mary has her own chair, fixed position. Other two females around the table can sit in 2 ways: the first to the left of Mary and the second to the right or vise-versa. Now, if 3 males will sit between them then no two female or two male will sit next to each other (female-male-female-male-female-male). But these males on their spots can also sit in different ways, namely in 3! different ways, so total 2*3!=12.

Answer B.


Lets first sit the 3 man, 2! ways.

Now since one position is fixed for women, there are 2 women left and they have 2! ways

2! X 2! = 4 answer is diff this way.

or shall we give possibility of 3 ways for women to be fixed with back facing so 3! ways, Lets discuss the doubt.

If u like my way of discussion plz give Kudos.


Since Mary's position is fixed men can be seated in 3! ways not in 2! ways. Would be easier to draw a circle and count the possible arrangements.
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BoburMirzo26
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Re: How many ways are there for 3 males and 3 females to sit [#permalink] New post   14 Jan 2020, 05:12
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(For those who always feel that there is some hidden gmat type of surprize) ultra tricky question in a way that special restriction (Mary's fixed place) is not even a restriction. Number of ways these people would sit around the table with Mary going round is repetitive and should be anyways taken out.
Let's fix females first -> according to formula (3-1)!=2!
It would have been 2! for males too, if not the fact that they are sitting in a big circle together with women. Thus we have 3!
3! 2! = 12
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KunalShinde
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Re: How many ways are there for 3 males and 3 females to sit [#permalink] New post   25 Oct 2023, 12:40
How many different possibilities are there if Mary’s position is not fixed?

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Re: How many ways are there for 3 males and 3 females to sit [#permalink]
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