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A tea party is arranged for 16 people along two sides of a long table with 8 chairs each side. four persons wish to sit on one particular and two on other side. in how many ways they all can be seated?

now for four persons can sit on either side. so 2 ways for them, and can be arranged in $P_{4}^{8}$ ways. now other two persons can sit on other side which in $P_{2}^{8}$ ways. for remaining people can be sit in 10! ways. so in all i get answer by multiplying all these. but my textbook misses out factor 2 in answer, rest everything is same. can you tell me where's the problem

thanks

Taylor Ted
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    No a particular sides means either left or right. The direction is fixed. – Archis Welankar Apr 10 '17 at 05:44
  • @ArchisWelankar OKAY THANKS – Taylor Ted Apr 10 '17 at 05:59
  • @TaylorTed This is more a question of language than maths. You appear to have assumed that the four people want to sit on the same side but it could be either side. The book appears to have assumed that they not only want to sit on the same side but also they want a specific side. I would interpret the problem as the book does. – badjohn Apr 10 '17 at 10:23

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