A table has provision for 7 seats, 4 being on one side facing the window and 3 being on the opposite side. The number of ways in which 7 people can be seated at the table if 2 people, X and Y, must sit on the same side, is

detailed solution

Correct option is B

When X and Y sit on the side facing the window—First, we have to select 2 persons for the side facing the window and 3 for the opposite side from the remaining 5. The number of selections for this is equal to  5C2×3C3.For each of the selections, the number of arrangements = 4! × 3!.∴ The number of ways to sit when X, Y are on the side facing the window =5C2×3C3×4!×3!.When X and Y sit on the other sideAs before, the number of ways to sit=5C1×4C4×4!×3!∴ Required number of ways=5C2×3C3×4!×3!+5C1×4C4×4!×3!=5×42×1×24×6+5×1×24×6=2160