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- Homework Statement
- Eighteen guests have to be seated, half in each side of a long table. Four particular guests desire to sit on 1 particular side and the three others on the other side. Determine the no of ways in which sitting arrangement can be done

- Homework Equations
- no of arrangements =nPr

4 guests want to be seated on one particular side.

So we choose 4 out of 9 seats on that particular side for them i.e 9C4. And they can arrange among themselves in 4! Ways.

So 9C4*4!

The we choose 3 out of 9 seats on the other side for the three people 9C3

They can arrange themselves in 3! Ways.

So 9C3*3!

Now the rests of the people can choose the 11 left seats and arrange themselves in 11! Ways

Therefore total no. of seating arrangements = 9C4*4! *9C3*3! * 11!

But thus isn't the correct answer.

Please tell me what is wrong with my approach

So we choose 4 out of 9 seats on that particular side for them i.e 9C4. And they can arrange among themselves in 4! Ways.

So 9C4*4!

The we choose 3 out of 9 seats on the other side for the three people 9C3

They can arrange themselves in 3! Ways.

So 9C3*3!

Now the rests of the people can choose the 11 left seats and arrange themselves in 11! Ways

Therefore total no. of seating arrangements = 9C4*4! *9C3*3! * 11!

But thus isn't the correct answer.

Please tell me what is wrong with my approach

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