Mathematics 9709 · AS & A Level · Permutations and combinations
Permutations and combinations — practice question
Mr and Mrs Ahmed, together with their two children, and Mr and Mrs Baker, together with their three children, are going to an activity centre as a group. For some activities, they will be split into separate groups.
(a)[2]
How many different ways can the $9$ people be split into one group of $6$ and one group of $3$?
(b)[3]
A random selection of $5$ out of the $9$ people is made for one activity. Find the probability that this group of $5$ includes all $3$ Baker children.
(c)[3]
All $9$ people are arranged in a straight line. Find the number of different line-ups in which Mr Ahmed is not beside Mr Baker.
(d)[3]
Find the number of different line-ups in which exactly one person stands between Mr Ahmed and Mr Baker.
Worked solution & mark scheme
This 11-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Correct combinatorial calculation $^9C_6\times3!$ or an equivalent form” …