Mathematics 9709 · AS & A Level · Sampling and estimation

Sampling and estimation — practice question

Four families visit a theme park together. Mr and Mrs Lin bring their $2$ children. Mr O’Connor brings his $2$ children. Mr and Mrs Ahmed bring their $3$ children. Mrs Burton brings her son. The $14$ people must all pass through a turnstile one at a time to enter the theme park.
(i)[3]

How many different sequences are possible for the $14$ people to pass through the turnstile if each family remains together?

(ii)[3]

How many different sequences can the $8$ children and $6$ adults take through the turnstile if no two adults are consecutive?

(iii)[3]

After entering the theme park, the children ride the roller-coaster. Each roller-coaster car takes $3$ people. In how many different ways can the $8$ children be split into two groups of $3$ and one group of $2$ for the roller-coaster?

Worked solution & mark scheme

This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: Correct expression $4! \times 3! \times 5! \times 2! \times 4!$ (not in denominator)

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