When is a permutation used?

Use permutations when order matters, and combinations when only the set of chosen items matters.

How is a togetherness condition handled?

Bind the two people into one block, arrange the block, then multiply by 2 for their swap.

When must a factorial be divided out?

Divide by the factorial of the number of groups when the groups are not labelled.

S5 Mathematics: Permutations and Combinations Practice Paper 1

2026-11-03

Tutor Prep Guide · Secondary Mathematics

Set one separates ordered from unordered selections: full arrangements and C(5,2) first, then multi-role choices, mixed groups and the block method, then repeated letters and unlabelled groups, ending with the error of answering 15 instead of 30.

Quick answer　24, 10, 30, 6, 56, 30, 1 440, 280, 554 400 and 30.

01　Paper details (check answers afterwards)

Item	Detail
Questions	10 questions
Suggested time	25 minutes
Difficulty mix	Foundation 4 · Intermediate 3 · Challenge 2 · Error redo 1
Chapter	Chapter: S5 Mathematics: Permutations and Combinations – Tutor Lesson Plan
Level	S5

02　Questions (10 items)

FoundationFour students stand in a line. How many different orders are possible?
FoundationHow many ways are there to choose 2 books from 5 different books?
FoundationFrom 6 people, pick a chairperson and a vice-chairperson who cannot be the same person. How many outcomes?
FoundationHow many arrangements are there of the three letters A, B and C?
IntermediateHow many 3-person teams can be formed from 8 students?
IntermediateFrom 5 boys and 3 girls, choose 2 boys and 1 girl. How many combinations?
IntermediateSeven people queue up with A and B standing next to each other. How many orders are possible?
ChallengeNine people are split into three groups of 3, with the groups unlabelled. How many ways?
ChallengeHow many distinct arrangements are there of all 11 letters in STATISTICS?
Error redoFrom 6 people, choose 2 where one writes the report and one presents it. How many arrangements?

03　Answers and one-line notes

#	Answer	One-line note
1	24 orders	Multiply 4 x 3 x 2 x 1, which is 4 factorial.
2	10 ways	Order does not matter, so use C(5,2), which is 10.
3	30 outcomes	That is 6 x 5, because the two roles are different.
4	6 arrangements	It is 3 factorial, that is 3 x 2 x 1 = 6.
5	56 teams	C(8,3) is 8 x 7 x 6 divided by 6, giving 56.
6	30 combinations	Take C(5,2) times C(3,1), which is 10 x 3 = 30.
7	1 440 orders	Treat A and B as one block so there are 6! orders, times 2 for swapping them, giving 1 440.
8	280 ways	That is C(9,3) x C(6,3) x C(3,3) divided by 3!, which is 280.
9	554 400 arrangements	Divide 11! by 3! x 3! x 2!, which is 39 916 800 divided by 72.
10	30 arrangements	The roles differ, so order matters and the answer is 30, not the 15 of C(6,2).

04　What to do after marking

After marking, redo only the wrong items and write down which step went wrong (formula, unit, or misread number).
Repeat the same item two days later; move to the next paper only when both attempts are correct.
Parents only need the answer and note columns; there is no need to explain every item.

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