Mathematics 9709 · AS & A Level · Permutations and combinations
Permutations and combinations — practice question
Raman and Sanjay are two of the $9$ people in a quiz team altogether. Two photographs of the quiz team are to be taken. In the first photograph, the $9$ members are arranged in a straight line.
(a)[1]
How many distinct arrangements of the $9$ members are there if Raman is placed at the centre of the line?
(b)[3]
How many distinct arrangements of the $9$ members are there if Raman and Sanjay are not adjacent?
(c)[2]
In how many different ways may the $9$ members be split into a group of $5$ and a group of $4$?
(d)[4]
For a random split into a group of $5$ and a group of $4$, find the probability that Raman and Sanjay are in the same group.
Worked solution & mark scheme
This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Correct calculation of $8! = 40320$.” …