Worksheets — Set 1

Graph theory & combinatorics · Counting and combinatorics

Print and write your answers. Use diagrams to show thinking.

Warm-up

1. How many subsets does a set with 5 elements have? ___ 2. Prove or disprove: if n is even, n² is even. 3. P(at least one head in 4 fair tosses) = ___

_See printable PDF for diagram._

Written practice

1. How many subsets does a set with 4 elements have? ___ 2. Prove or disprove: if n is even, n² is even. 3. P(at least one head in 3 fair tosses) = ___ 4. Write the recurrence aₙ = 3aₙ₋₁ with a₀ = 1 ___ 5. Graph with 5 vertices — minimum edges for connectivity? ___ 6. Convert 43₁₀ to base 4. = ___ 7. How many subsets does a set with 7 elements have? ___ 8. P(at least one head in 6 fair tosses) = ___

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More written practice

1. Write the recurrence aₙ = 6aₙ₋₁ with a₀ = 1 ___ 2. Graph with 8 vertices — minimum edges for connectivity? ___ 3. Convert 46₁₀ to base 7. = ___ 4. How many subsets does a set with 10 elements have? ___ 5. P(at least one head in 9 fair tosses) = ___ 6. Write the recurrence aₙ = 9aₙ₋₁ with a₀ = 1 ___

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Patterns and rules

1. How many subsets does a set with 21 elements have? ___ 2. Prove or disprove: if n is even, n² is even. 3. P(at least one head in 20 fair tosses) = ___

_See printable PDF for diagram._

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Parent tip: Use trees or tables for counting