Permutations #4
Probability
Level
4
A tea party is arranged for 16 persons along two sides of a long table with 8 chairs on each side. Four persons wish to sit on one particular side and two on the other side. In how many ways can they be seated?
The answer is 341397504000.
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1 solution
Let the persons be P1, P2,P3, P4, P5, P6, P7, P8 and Pi, Pii Piii, Piv, Pv, Pvi, Pvii, Pviii.
Here, the order of seating arrangement is as below :-
4 persons ( P1, P2,P3, P4 ) wish to sit on one side in any of the 8 chairs.
2 persons ( Pi, Pii) wish to sit at other side in any of the 8 chairs.
Rest 10 persons can sit at any of the remaining 10 chairs.
Now,
4 persons can be arranged in 8 chairs in N1 = 8P4.
2 persons can be arranged in 8 chairs on the other side of the table in N2 = 8P2.
Rest 10 persons can be arranged in remaining 10 chairs (after sitting arrangement of above 6 persons are complete ) in N3 = 10P10.
Hence, the required number of seating arrangements is :-
=> N1 x N2 x N3.
=> 8P4 x 8P2 x 10P10