How many ways are there for 3 males and 3 females to sit : GMAT Problem Solving (PS)
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# How many ways are there for 3 males and 3 females to sit

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

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18 Dec 2010, 04:18
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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
[Reveal] Spoiler: OA
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18 Dec 2010, 05:22
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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.

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20 Sep 2013, 00:34
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.

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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20 Sep 2013, 00:43
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.

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

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13 Nov 2014, 15:09
Hello from the GMAT Club BumpBot!

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

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11 Aug 2016, 21:24
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: How many ways are there for 3 males and 3 females to sit   [#permalink] 11 Aug 2016, 21:24
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