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 $8! = 40320$.

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