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Ask iit jee aieee pet cbse icse state board community Community Discussion Question: permutations n combinations
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anki016 (40)

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find da no of ways in which seven boys can sit  on a round table if they sdhn't have da same neighbours in any two arragements?????

    
a_JOSHI (167)

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i think it should be 1/2( 6!)
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anki016 (40)

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it is but plz explain me......... i m failing to analyse it
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chinnu (83)

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total no. of arrangements r 6!
of which a person can have same neighbours twice.
hence the ans is 6!/2
rate me if m correct.
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learner (325)

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Perfect answers by chinnu and a_JOSHI....


Circular permutations of n objects are (n - 1) !..


Now, consider A,B,C,D,E,F,G to be the seven boys..


consider case of boy D..his neighbours are C and E..


In another arrangement, neighbours should be different..


Thus, both C-D-E  and E-D-C cant exist together..


So, for each boy,there are two arrangements wherein neighbours are the same..


So, (n-1)! has to be divided by 2..


Thus we get 6! / 2..

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a_JOSHI (167)

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yea see the total no. of ways that ppl can sit around a table is (n-1)! so here it'll be 6! and since two guys can be next to the person...so tht same guy can be there twice...so for once we divide it by 2
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