Question

Eight guests have to be seated 4 on each side of a long table. 2 particular guests desire to sit on one side of the table and 3 on the other side. The number of ways in which the sitting arrangements can be made is

Answer 1

Let the two particular guests sit on right side.
So the three particular guests will sit on left side.

So remaining will be 3 people which need to be selected.
From these 3 people 2 will sit on right side and the one will sit on left side.

Total ways of selecting the remaining will be =
³C₂ ⨯ ¹C₁ = 3

Total ways of arranging the people will be =

Selection of remaining × 4! ( for arranging people on left side) × 4! ( arranging people on right side) =
3 × 24 × 24 = 3 × 576 = 1728

So in 1728 ways we can arrange them

Answer 2

Answer:

3 × 4! × 4! = 3 × 24 × 24 = 1728

(B) ---------> 1728

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