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Question

in how many ways can 7 people be seated at a round table if 12 particular people must not sit next to each other?

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Solution

REF. Image.
7 boys on a round table
n!n [for n boys]
[ round table]
PTotal=6!
PTotal=7!7
For 2 boys together
consider a block arrangement
5!×2! permutation
=240
P2boys together
6!×2!6=P2 boys together
For 2 particular boys apart,
PTotalP2 boys together
=6!5!×2
=4×5!
=480

1063668_876535_ans_863d0d3fb2c54f7db159fafea5cfab89.png

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