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January 28th, 2012, 09:58 PM  #1 
Member Joined: Jan 2012 Posts: 72 Thanks: 0  Permutation and combinations (seating)
A particular project work group of 2 girls and 2 boys meets for regular project discussions at a round stonetable with 5 secured seats. find the number of ways the members of this group could be seated if they do not mind who they are sitting with. What is wrong with 5x4x3x2=120? 
January 28th, 2012, 11:57 PM  #2 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,923 Thanks: 1123 Math Focus: Elementary mathematics and beyond  Re: Permutation and combinations (seating)
Why do you think that answer is wrong?

January 29th, 2012, 12:55 AM  #3 
Member Joined: Jan 2012 Posts: 72 Thanks: 0  Re: Permutation and combinations (seating)
the correct answer is 24

January 29th, 2012, 01:18 AM  #4 
Member Joined: Jan 2012 Posts: 31 Thanks: 0  Re: Permutation and combinations (seating)
That's a good reason to think it's wrong. haha

January 29th, 2012, 01:25 AM  #5 
Member Joined: Jan 2012 Posts: 31 Thanks: 0  Re: Permutation and combinations (seating)
Is there anything wrong with using the mn rule? 4 x 3 x 2 x 1 = 24. The fact that there is one extra chair doesn't stop them from being seated consecutively. So why wouldn't it just be finding there different ways that four people can be seated. Or for instance can be placed in a running race. 4 x 3 x 2 x 1 = 24. David. 
January 29th, 2012, 04:23 AM  #6 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,923 Thanks: 1123 Math Focus: Elementary mathematics and beyond  Re: Permutation and combinations (seating)
If you have five empty chairs and one person, how many ways can that person be seated?

January 29th, 2012, 04:45 AM  #7 
Member Joined: Jan 2012 Posts: 31 Thanks: 0  Re: Permutation and combinations (seating)
5?

January 29th, 2012, 04:49 AM  #8 
Member Joined: Jan 2012 Posts: 31 Thanks: 0  Re: Permutation and combinations (seating)
Ok, so you're saying the correct answer is 5x4x3x2x1 ?

January 29th, 2012, 05:14 AM  #9 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,923 Thanks: 1123 Math Focus: Elementary mathematics and beyond  Re: Permutation and combinations (seating)
It certainly doesn't seem to make sense any other way. Sure, you can seat four persons consecutively, but what about the fifth chair? The fact that two of the people are boys and two are girls doesn't matter, I think. On another note combinations and permutations have never been a strong point of mine. 
January 29th, 2012, 10:11 AM  #10 
Newbie Joined: Nov 2011 Posts: 7 Thanks: 0  Re: Permutation and combinations (seating)
I agree with 120. If they always keep the same seat empty at the round table it would be 4! or 24 ways. But if they are allowed to change which seat is open, then you have 5 instances of 24 ways, or 120 ways for them to be seated. I don't know what is meant by 5 secured seats but maybe that changes the situation to make the answer be 24. 

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