Unit 1: Number and Algebra
Topic 1.10: Counting & binomial (HL only) Questions
Practice 20 exam-style questions for IB Math AA SL Topic 1.10. Review the question stems below, then unlock the full Question Bank to access markschemes, model answers, and AI grading.
11 mark
2026
How many ways can 5 books be chosen from a shelf of 12 books?
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2026
A 3-letter code uses different letters from A–F in alphabetical order. How many codes?
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2026
5 athletes run a race with no tied finishes.
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2026
Why is 'arrange these in increasing order' a selection (ⁿCᵣ), not an arrangement (ⁿPᵣ)?
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2026
In how many ways can all 4 distinct letters of a word be rearranged?
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2026
8 different toppings are available. A customer chooses 3 different toppings for a pizza. Find the number of possible pizzas.
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2026
State the values of x for which the expansion of (1 − 5x)⁻² is valid.
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2026
A group of 3 from 8 must include a chairperson. How many groups?
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Write down the values of for which the expansion of is valid.
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2026
A group of 4 from 9 must NOT include one particular person. How many groups?
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8 people stand in a line. How many different orders are possible?
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2026
Find the coefficient of x⁴ in the expansion of (1 + x)⁷.
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For which values of x is the expansion of (1 + 3x)⁻¹ valid?
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State the values of x for which the expansion of (1 + 4x)⁻¹ is valid.
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2026
From a class of 20 students, 2 are chosen to represent the class. Find the number of possible pairs.
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2026
4 people sit in a row and 2 of them must sit together. How many arrangements?
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2026
Using (1 + x)⁻¹ ≈ 1 − x + x² to estimate 1/1.05, which x do you use?
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