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# Seven men and seven women have to sit around a circular

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Manager
Joined: 07 Jun 2006
Posts: 113
Followers: 2

Kudos [?]: 8 [0], given: 0

Seven men and seven women have to sit around a circular [#permalink]  23 Oct 2006, 10:04
Seven men and seven women have to sit around a circular table so that no 2 women are together. In how many different ways can this be done?

I think I have posted this before but wanted to post it again as I am not gettign ney idea to solve it.
SVP
Joined: 01 May 2006
Posts: 1798
Followers: 8

Kudos [?]: 102 [0], given: 0

Possibility = 7*7 * 6*6 * 5*5 * 4*4 * 3*3 * 2*2 * 1*1 = (7!)^2

We choose:
1 man among 7 and 1 woman among 7,
then, 1 man among 6 and 1 woman among 6
then, 1 man among 5 and 1 woman among 5
... and so on.
Senior Manager
Joined: 08 Jun 2006
Posts: 341
Location: Washington DC
Followers: 1

Kudos [?]: 26 [0], given: 0

I think the answer is 7! * 6!

Explanation -
7 men can be arranged in a circular table in (7 -1)! = 6! ways
Women should sit in the gaps between two men so that no 2 women are together.
There are 7 gaps. So women can arrange themselves in 7! ways.

Possible ways = 7! * 6!
Senior Manager
Joined: 01 Sep 2006
Posts: 301
Location: Phoenix, AZ, USA
Followers: 1

Kudos [?]: 15 [0], given: 0

7!*7! [#permalink]  24 Oct 2006, 16:27
14 places around the table
Wmen can pick 7 plcaes leaving 1 seat so total ways 7!
Men can sit in between the women 7!
7!*7!   [#permalink] 24 Oct 2006, 16:27
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