On six seating chairs including one red chair around a big round table

Question

On six seating chairs including one red chair around a big round table , A, B, C, D, E, F each sit on a chair. A must sit on the red chair and B must be beside A. How many seating arrangement are?
 A. 36 B. 40 C. 44 D. 48 E. 64

Senthil1981 · Answer

Since the Red chair is fixed (assuming) for A, then it's simple to calculate for the remaining 5 people.
B has 2 choices and the rest have 4! ways of sitting,
so no. of seating arrangements = 2 * 4! = 2 * 24 = 48

abhimahna · Answer

Lets fix A at its red chair.

Now, consider B is on the left of A. Other people can take any option out of the pending four.

So, number of ways = 4!

Consider B is on the right of A. Similar to above, number of ways = 4!

Total ways = 4! + 4! = 48. Hence, D

MathRevolution · Answer

==> If you set A, and B sits on the left side of A, the rest can be seated with the number of cases of 4*3*2*1=24. If B sits on the right side of A, there can be 24 number of cases that they can be seated. Hence, 24+24=48. The answer is D.
Answer: D

Abhishek009 · Answer

Seating.jpg No of ways of Placing A = 1 ( Fixed ) No of ways of Placing B = 2 ( On either side of A ) No of ways of Placing C = 4 No of ways of Placing D = 3 No of ways of Placing E = 2 No of ways of Placing F = 1 So , Total number of ways is = No of ways of Placing A * No of ways of Placing B * No of ways of Placing C - F Or, Total number of ways is = 1*2*4! Or, Total number of ways is = 48 Hence answer will be (D) 48

AbhijitGoswami · Answer

Hi Abhishek,

Why not (n-1)! for rest 4 people C to F?

-Abhijit

abhimahna · Answer

For the rest of the 4 people, we are not taking (n-1)! because remember in a circular arrangement we fix the position of one person and arrange the rest using (n-1)! and in this question, we have already fixed the position of A. So, the remaining people would be arranged taking A as reference.

I hope it is clear now.

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On six seating chairs including one red chair around a big round table

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On six seating chairs including one red chair around a big round table

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