Inclusion exclusion

• How to Distribute Identical Stones Among Buckets with Limits
  Count distributions of identical stones into distinct buckets with minimum and maximum limits using stars and bars, inclusion-exclusion, or generating functions.
• How to Count Elements Divisible by Exactly Two of Three Numbers
  To count elements divisible by exactly two of three divisors, add the three pairwise counts and subtract three times the count divisible by all three.