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At a round table, there should be 10 people seated. Determine the total number of arrangements if 2 specific individuals among them are not to stand side by side. 

Option: 1

362880
 


Option: 2

806400


Option: 3

282240

 


Option: 4

462890


Answers (1)

best_answer

Given that,

There are 10 people seated at a round table.

The 10 people are seated around a round table at 9! ways.

Thus,

\mathrm{ \begin{aligned} & 9 !=9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \\ & 9 !=362880 \end{aligned} }

The number of ways in which 2 people sit side by side is given by,
8 ! \times 2 !=8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 2 8 ! \times 2 !=80640

Thus, the total number of arrangements is,

9 !-8 ! \times 2 !=362880-80640

9!-8 ! \times 2 !=282240

Therefore, the number of ways the arrangements are done in 282240 ways.

Posted by

seema garhwal

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