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CAIE A-Level Mathematics 5.2 Permutations and Combinations Question Bank

Practise counting arrangements and selections with repeated objects, fixed positions, adjacency restrictions and case conditions by choosing permutations or combinations correctly.

Syllabus
2028–2030
Course
Mathematics 9709
Level
AS

Exam points

  • divide factorial arrangements by repeated-object factorials before applying position restrictions
  • use combinations for unordered selections and split minimum or maximum conditions into valid cases
  • count the unrestricted set and subtract arrangements that violate adjacency or grouping rules

Covered syllabus points

5.2.1—Permutations and combinations5.2.2—Arrangement restrictions

5.2 Permutations and combinations question 1

[Maximum number: 6]

Raman and Sanjay are members of a quiz team which has 9 members in total. Two photographs of the quiz team are to be taken.

For the first photograph, the 9 members will stand in a line.

Question (a)

(a)

How many different arrangements of the 9 members are possible in which Raman will be at the centre of the line?

[ 1 ]

Question (b)

(b)

How many different arrangements of the 9 members are possible in which Raman and Sanjay are not next to each other?

[ 3 ]

Question (c)

(c)

For the second photograph, the members will stand in two rows, with 5 in the back row and 4 in the front row.

In how many different ways can the 9 members be divided into a group of 5 and a group of 4?

[ 2 ]
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