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Offlinerobbyberto
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Anyone know how to do this?
    #7634167 - 11/14/07 09:17 AM (16 years, 2 months ago)

It sounds simple but I cannot figure out this question.

How many ways can nine people be seated in nine chairs if two of the people refuse to sit next to each other?


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“People say having kids is life changing, well that doesn’t necessarily mean a good thing, does it? I could take one of my legs off. That would change my life.” -Karl Pilkington



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InvisibleWhiskeyClone
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Re: Anyone know how to do this? [Re: robbyberto]
    #7634279 - 11/14/07 09:58 AM (16 years, 2 months ago)

Infinite ways unless you specify how the chairs are arranged.


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Welcome evermore to gods and men is the self-helping man.  For him all doors are flung wide: him all tongues greet, all honors crown, all eyes follow with desire.  Our love goes out to him and embraces him, because he did not need it.

~ R.W. Emerson, "Self-Reliance"

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Offlinerelativexistance
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Re: Anyone know how to do this? [Re: robbyberto]
    #7634583 - 11/14/07 11:24 AM (16 years, 2 months ago)

assuming all the 9 chairs are stationary and aligned next to one another in a row, by my calculations there are 282,240 possible combinations.

im pretty confident with that number and i'll explain how i came up with it.

first off i considered the other 7 people, forgetting about the 2 that won't sit next to one another. there are 7 chairs and 7 people, the number of combinations they can sit is 7! since there are no restrictions to them sitting.

now considering the 2 that dont sit together.
imagine the first person sitting in the farthest left seat. the second person has to sit at least 1 seat apart. with the first person in the farthest left seat say "seat 1", the second person can only sit in 7 other seats as seat 2 is unoccupiably by person 2, so that 7 possible combinations. now move the first person into seat #2. now the second person can only sit in 6 possible seats as seat 2 is occupied by person 1 and seat 3 is not allowed. continue on with this pattern and you have the following.

(7+6+5+4+3+2+1)*2*7! = 282,240

the multiplication by 2 factors in when person 1 and person 2 are switched in the above scenario used to calc the 2 person combinations.


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Offlinerobbyberto
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Re: Anyone know how to do this? [Re: relativexistance]
    #7634985 - 11/14/07 12:51 PM (16 years, 2 months ago)

Thanks for the good explanation and yes I believe that is the right answer. God I hate math.


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“People say having kids is life changing, well that doesn’t necessarily mean a good thing, does it? I could take one of my legs off. That would change my life.” -Karl Pilkington



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