count-combinations

When to Use

• Probability calculations
• Counting permutations or combinations
• Enumerating all possibilities (brute force)
• Monte Carlo simulation
• Card game probabilities
• Dice roll distributions
• Urn/ball problems

When NOT to Use

• When closed-form formula exists and is simpler
• Astronomically large sample spaces (use simulation)
• When approximation is acceptable (use sampling)

The Pattern

Define sample space explicitly, then count favorable outcomes.