- [Maximum mark: 6]
A self‑service sushi restaurant has a row of 12 available seats, as shown in the following diagram. [Diagram shows 12 empty seats in a row.]
Anvi, Vanya and Parita decide to go to the restaurant for lunch.
(a) Find the number of possible ways that they can be seated in this row, if they decide not to sit together as a group of 3. [3]
The next day, Anvi, Vanya and Parita are joined by 3 additional people in the same restaurant, and they sit in the same row of 12 available seats. Anvi, Vanya and Parita now decide to sit next to each other as a group of 3.
(b) Find the number of possible ways that these 6 people can be seated. [3]