My Math Forum Permutation and combinations (seating)

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January 29th, 2012, 11:27 AM   #11
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Re: Permutation and combinations (seating)

Quote:
 I don't know what is meant by 5 secured seats . . .
My guess is that means the seats cannot be moved.

 January 30th, 2012, 12:29 AM #12 Senior Member   Joined: Apr 2011 From: USA Posts: 782 Thanks: 1 Re: Permutation and combinations (seating) Order matters so it's a permutation. The empty seat has nothing to do with it and there's no stipulation about whether some particular chair has to remain empty. $\text{P\binom{5}{4}= \frac{5!}{(5-4)!} = 120}$
 January 30th, 2012, 03:35 AM #13 Senior Member   Joined: Jul 2011 Posts: 245 Thanks: 0 Re: Permutation and combinations (seating) I like how you sound so definitive, Erimess. lol.
 January 31st, 2012, 12:18 AM #14 Senior Member   Joined: Apr 2011 From: USA Posts: 782 Thanks: 1 Re: Permutation and combinations (seating) Well... LOL. I just have to hope my definitiveness means I'm right. (If I'm not too sure, I do try to be honest about that.)
January 31st, 2012, 01:29 AM   #15
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Re: Permutation and combinations (seating)

Quote:
 Originally Posted by Erimess Order matters so it's a permutation.
An application of the factorial accounts for all possible orderings, if I'm not mistaken.

$5!\,=\,120$

January 31st, 2012, 10:48 PM   #16
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Re: Permutation and combinations (seating)

Quote:
Originally Posted by greg1313
Quote:
 Originally Posted by Erimess Order matters so it's a permutation.
An application of the factorial accounts for all possible orderings, if I'm not mistaken.

$5!\,=\,120$
Well, yes. Habit. If it had been 4 chairs I probably would've done it that way. (I can think of having extra people, but can't manage to turn it around and think of extra chairs. :P )

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### project work in permutation and combinationsn

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