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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.   <div cla

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

46289


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,

\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,


\begin{aligned} &8 ! \times 2 !=8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 2\\ &8 ! \times 2 !=80640 \end{aligned}

Thus, the total number of arrangements is,


\begin{aligned} &9 !-8 ! \times 2 !=362880-80640\\ &9 !-8 ! \times 2 !=282240 \end{aligned}

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

 

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