IB Maths AA HL May 2024 TZ1 Past Paper 1 Q 9.
A group of 10 children includes one pair of brothers, Alvin and Bobby, and one pair of sisters, Catalina and Daniela.
The children are to be seated at 10 desks which are arranged in two rows of five as shown in the following diagram.
Alvin and Bobby must be seated next to each other in the same row.
(a) Find the total number of ways the children can be seated.
After an argument, Catalina and Daniela must not be seated next to each other. Alvin and Bobby must still be seated next to each other.
(b) Find the total number of ways the children can be seated.