Permutation and Combination: JAMB Mathematics Questions, Answers & Notes

What Permutation and Combination covers in the JAMB Mathematics syllabus

Counting problems use factorials, permutations and combinations. A factorial n! = n × (n−1) × ... × 1, and 0! = 1. Use permutations when the order matters (arrangements): ⁿPᵣ = n!/(n−r)!. Use combinations when order does not matter (selections): ⁿCᵣ = n!/[r!(n−r)!]. Useful facts: ⁿC₀ = ⁿCₙ = 1, and ⁿPᵣ = ⁿCᵣ × r!. The key skill is reading the problem: 'arrange in a row', 'order', 'prizes ranked' → permutations; 'choose a committee', 'select', 'group' → combinations.

For Permutation and Combination, JAMB expects you to be able to:

• Evaluate factorials and use ⁿPᵣ and ⁿCᵣ
• Decide whether a problem needs permutations (order matters) or combinations (order does not)
• Solve counting and selection word problems

Key facts & revision notes: Permutation and Combination

These are the recurring points our Permutation and Combination questions test — revise them until each feels automatic, then practise the questions above to lock them in.

• = 5 × 4 × 3 × 2 × 1 = 120.
• Number of arrangements = 4!
• ⁿPᵣ = n!/(n−r)!; ⁵P₂ = 5!/3!
• ⁿCᵣ = n!/[r!(n−r)!]; ⁵C₂ = (5×4)/(2×1) = 10.
• Permutations count arrangements where the order matters.
• Combinations count selections where the order does not matter.
• ⁶C₃ = (6×5×4)/(3×2×1) = 120/6 = 20.
• Choosing 0 items from n can be done in exactly 1 way, so ⁿC₀ = 1.
• Choosing all n items can be done in exactly 1 way, so ⁿCₙ = 1.
• ⁷C₅ = ⁷C₂ = (7×6)/(2×1) = 21.
• 3 distinct letters give 3!
• Order doesn't matter, so ⁵C₂ = 10.
• Since order matters for permutations: ⁿPᵣ = ⁿCᵣ × r!.
• ⁶C₂ = (6 × 5)/(2 × 1) = 15.
• Choosing 1 item from n can be done in n ways.
• 120/(6 × 2) = 120/12 = 10.
• Arranging all n items gives n!
• ⁸C₆ = ⁸C₂ = (8 × 7)/2 = 28.
• ⁵C₃ = 10 (order does not matter).

Worked examples

Three Permutation and Combination questions with the answer and a short explanation, so you can see how the topic is set before you practise the full set.

How Permutation and Combination is tested in JAMB Mathematics

Our Permutation and Combination bank holds 40 questions (12 easy, 21 medium, 7 hard). JAMB Mathematics typically returns to Permutation and Combination year after year, so steady practice on this topic is high-value revision. Questions are multiple-choice with four options, and at UTME pace you get roughly 40 seconds each — which is why timed practice matters.

How to answer Permutation and Combination questions

Work the stem first and predict the answer before you look at the options; then eliminate the ones that contradict the key facts above. Watch for “which is not…”, “all of the above” and “except” style stems, which are where rushed candidates lose easy marks on Permutation and Combination. If a calculation or a precise definition is involved, work it from first principles rather than guessing from a half-remembered rule. When two options look right, re-read the stem for the qualifier that separates them — JAMB rarely repeats an option by accident. If you are still unsure, eliminate the two weakest choices to lift your odds, flag the question, and move on; never burn a full minute on one Mathematics item when the exam gives you about forty seconds each. Then come back to flagged questions with whatever time remains. The single most reliable way to get faster at Permutation and Combination is repeated timed practice, so use the button above until the recurring patterns feel automatic.

Common mistakes to avoid in Permutation and Combination

The errors that cost marks on Permutation and Combination are usually careless rather than conceptual: misreading a negative stem, confusing two similar terms, or rushing a definition you actually know. Candidates also over-rely on “expo” and last-minute cramming instead of understanding the topic — which fails the moment JAMB rephrases a familiar idea. Treat every option as a claim to be checked against the facts above, keep your working tidy for any calculation, and don’t change a considered answer on a hunch. Above all, revise Permutation and Combination actively by answering questions, not just by re-reading notes — recall under time is what the exam rewards.

Frequently asked questions

Is Permutation and Combination part of the JAMB Mathematics syllabus?

Yes. Permutation and Combination is a recognised topic in the JAMB Mathematics syllabus, covering evaluate factorials and use ⁿPᵣ and ⁿCᵣ. You should be able to recall its key facts and apply them to multiple-choice questions.

How many Permutation and Combination questions can I practise on Belmadeng?

There are 40 original, JAMB-standard Permutation and Combination questions in our free bank, each with the correct answer and a worked explanation. You can practise them untimed or as a timed test.

What are the most important points to know about Permutation and Combination?

Counting problems use factorials, permutations and combinations. A factorial n! = n × (n−1) × ... × 1, and 0! = 1. Use permutations when the order matters (arrangements): ⁿPᵣ = n!/(n−r)!. Use combinations when order does not matter (selections): ⁿCᵣ = n!/[r!(n−r)!]. Useful facts: ⁿC₀ = ⁿCₙ = 1, and …

How do I answer Permutation and Combination questions quickly in JAMB?

Read the stem carefully, eliminate clearly wrong options, and match the remaining choices to the key facts for Permutation and Combination. Practising timed Permutation and Combination questions builds the speed you need for UTME's pace of about 40 seconds per question.

Are these JAMB Mathematics Permutation and Combination questions past questions or original?

They are original questions written to JAMB (UTME) standard and mapped to the official syllabus — not reproduced past papers. This keeps them legal to use freely while closely mirroring how the real exam tests the topic.

Where can I practise Permutation and Combination questions free without signing up?

Right here — tap “Start Permutation and Combination practice” on this page to begin instantly. Belmadeng's CBT practice is completely free and needs no sign-up, download or subscription.

About these questions: original, JAMB-standard items written from the official UTME Mathematics syllabus (last reviewed 2026-09-18). Belmadeng is an independent study platform and is not affiliated with JAMB. Spotted an error? Use the report link.