Mathematics 9709 · AS & A Level · Permutations and combinations
Permutations and combinations — practice question
A party of $15$ friends goes to an adventure park. There are four families in the party:
- 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
They reach the park in three cars, with $6$ people in one car, $5$ people in another car and $4$ people in the third car. The cars are driven by Mr Lizo, Mrs Martin and Mr Nantes respectively.
(a)[3]
How many distinct ways are there to split the other $12$ people of the group between the three cars?
(b)[3]
If Mr Lizo is first and each family remains together, how many different orders are possible for the $15$ friends as they go through the gate?
(c)[2]
How many different teams can be selected from the $15$ people so that the $3$ children all come from different families?
(d)[3]
How many ways are there to choose the team so that at least one of Mr Kenny or Mr Lizo is present?
Worked solution & mark scheme
This 11-mark question has a full step-by-step worked solution and mark scheme. One marking point: “A suitable combination expression, for instance $
{^{12}C_5}\times{^{7}C_4}$.” …