Question

21. A table has 7 seats, 4 being on one side facing the window and 3 being on the oppo
side. In how many ways can 7 people be seated at the table if
(i) two people, X and Y must sit on the same side
(ii) X and Y must sit on opposite sides
(iii) if 3 people, X, Y and Z must sit on the side facing the window?​

Answer 1

Answer:

2160

2880

576

Step-by-step explanation:

Total Seats = 7

Window facing = 4

opposite = 3

(i) two people, X and Y must sit on the same side

Two cases X & Y sitting on window Facing + X & Y Sitting on opposite sides

= ⁴P₂ * 5!   + ³P₂ * 5!

= 12 * 120  + 6 * 120

= 18 * 120

= 2160

(ii) X and Y must sit on opposite sides

X sits on window Seat  & Y on opposite   +  X sits on opposite  side & Y sits on Window

= 4 * 3 * 5!  +  3 * 4  * 5!

= 24 * 120

= 2880

iii) 3 people, X, Y and Z must sit on the side facing the window

⁴P₃ * 4!

= 24 * 24

= 576