Worksheets — Set 7
Graph theory & combinatorics · Graph algorithms and structures
Print and write your answers. Use diagrams to show thinking.
Warm-up
1. How many subsets does a set with 11 elements have? ___ 2. Prove or disprove: if n is even, n² is even. 3. P(at least one head in 10 fair tosses) = ___
_See printable PDF for diagram._
Written practice
1. How many subsets does a set with 10 elements have? ___ 2. Prove or disprove: if n is even, n² is even. 3. P(at least one head in 9 fair tosses) = ___ 4. Write the recurrence aₙ = 9aₙ₋₁ with a₀ = 1 ___ 5. Graph with 11 vertices — minimum edges for connectivity? ___ 6. Convert 49₁₀ to base 10. = ___ 7. How many subsets does a set with 13 elements have? ___ 8. P(at least one head in 12 fair tosses) = ___
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More written practice
1. Write the recurrence aₙ = 12aₙ₋₁ with a₀ = 1 ___ 2. Graph with 14 vertices — minimum edges for connectivity? ___ 3. Convert 52₁₀ to base 13. = ___ 4. How many subsets does a set with 16 elements have? ___ 5. P(at least one head in 15 fair tosses) = ___ 6. Write the recurrence aₙ = 15aₙ₋₁ with a₀ = 1 ___
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Patterns and rules
1. How many subsets does a set with 27 elements have? ___ 2. Prove or disprove: if n is even, n² is even. 3. P(at least one head in 26 fair tosses) = ___
_See printable PDF for diagram._
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Parent tip: Use trees or tables for counting