Combinatorics Helper

Solve counting problems systematically using combinatorial techniques. Covers permutations, combinations, pigeonhole principle, inclusion-exclusion, and generating functions.

Usage

Describe a counting problem to get a systematic solution with explanation of the technique used.

Examples

• "How many ways can I arrange 5 books on a shelf?"
• "In how many ways can I choose a committee of 3 from 10 people?"
• "Use inclusion-exclusion to count integers divisible by 2 or 3 up to 100"

Guidelines

• Identify whether order matters (permutation) or not (combination)
• Check for repetition — with or without replacement changes the formula
• Use the multiplication principle for sequential independent choices
• Apply inclusion-exclusion when counting overlapping sets
• Verify answers with small cases when possible