9709 P53 - Jun 2022 - Q7
2870
A group of 15 friends visit an adventure park. The group consists of four families.
- Mr and Mrs Kenny and their four children
- Mr and Mrs Lizo and their three children
- Mrs Martin and her child
- Mr and Mrs Nantes
The group travel to the park in three cars, one containing 6 people, one containing 5 people and one containing 4 people. The cars are driven by Mr Lizo, Mrs Martin and Mr Nantes respectively.
(a) In how many different ways can the remaining 12 members of the group be divided between the three cars?
In the park, the group enter a competition which requires a team of 4 adults and 3 children.
(c) In how many ways can the team be chosen from the group of 15 so that the 3 children are all from different families?
(d) In how many ways can the team be chosen so that at least one of Mr Kenny or Mr Lizo is included?
