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Seating arrangemen ts

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Seating arrangemen ts

by wallz06 » Thu Jul 09, 2009 5:34 am
What is the most efficient way to approach the following problem:

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?
a)3
b)4
c)6
d)12
e)24
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by Neo2000 » Thu Jul 09, 2009 6:27 am
As women have to sit in-between the men, arrange the men first

7 men can be arranged around a circular table in 6! ways

Now, there are 7seats for 6 women to sit in. They can sit in 7P6 ways

Therefore total number of ways = 6! x 7P6
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by wallz06 » Thu Jul 09, 2009 8:16 am
Can you help me understand your response. Why can 7 men not be arranged in 7! ways. Any why do you say for 6 women to sit in when the question says there are 7 women? I'm just trying to understand the logic. Thanks for your help.
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by Neo2000 » Thu Jul 09, 2009 8:21 am
You are arranging them around a circular table

The number of ways of arranging "n" things around a circle in (n-1)!

However, once the men have been arranged, its no longer a circular arrangement. You now have 7 empty places and 6 women to fill in those places
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by cameronwu » Thu Jul 09, 2009 8:40 am
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Last edited by cameronwu on Thu Jul 09, 2009 8:44 am, edited 1 time in total.
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by Neo2000 » Thu Jul 09, 2009 8:54 am
Crap! i read the Q as 7men and 6women

So 7men can be arranged around a table in 6! ways and there are 7 places for 7women to sit between the men = 7! ways

Your final answer has to be 6! x 7!
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by cameronwu » Thu Jul 09, 2009 9:10 am
Neo2000 wrote:Crap! i read the Q as 7men and 6women

So 7men can be arranged around a table in 6! ways and there are 7 places for 7women to sit between the men = 7! ways

Your final answer has to be 6! x 7!
This seems highly inaccurate given that the largest answer choice is 24.

6! x 7! = 720 * 5040 = a seven digit number. You're suggesting that there are over 3.6 million ways to do this? hmm.... i don't know the answer but i don't think that's right.
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by Neo2000 » Thu Jul 09, 2009 9:20 am
https://www.tutorvista.com/content/math/ ... ations.php

The last bit on the page confirms my approach.
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by cameronwu » Thu Jul 09, 2009 10:11 am
OP, what's up with the answer choices? The link confirms Neo's method.

Neo - the term 6! * 7! is also equal to 10!. Any relationship or just coincidence?
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