Worksheets — Set 20
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 24 elements have? ___ 2. Prove or disprove: if n is even, n² is even. 3. P(at least one head in 23 fair tosses) = ___
_See printable PDF for diagram._
Written practice
1. How many subsets does a set with 23 elements have? ___ 2. Prove or disprove: if n is even, n² is even. 3. P(at least one head in 22 fair tosses) = ___ 4. Write the recurrence aₙ = 22aₙ₋₁ with a₀ = 1 ___ 5. Graph with 24 vertices — minimum edges for connectivity? ___ 6. Convert 62₁₀ to base 23. = ___ 7. How many subsets does a set with 26 elements have? ___ 8. P(at least one head in 25 fair tosses) = ___
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More written practice
1. Write the recurrence aₙ = 25aₙ₋₁ with a₀ = 1 ___ 2. Graph with 27 vertices — minimum edges for connectivity? ___ 3. Convert 65₁₀ to base 26. = ___ 4. How many subsets does a set with 29 elements have? ___ 5. P(at least one head in 28 fair tosses) = ___ 6. Write the recurrence aₙ = 28aₙ₋₁ with a₀ = 1 ___
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Patterns and rules
1. How many subsets does a set with 40 elements have? ___ 2. Prove or disprove: if n is even, n² is even. 3. P(at least one head in 39 fair tosses) = ___
_See printable PDF for diagram._
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Stretch
1. How many subsets does a set with 48 elements have? ___ 2. Prove or disprove: if n is even, n² is even.
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Parent tip: Use trees or tables for counting