Lin Hsin Hsin Artificial Intelligence Center
FRONTIER MODELS
Combinatorics Explained
📖
The number of possible combinations from 300,000 words depends entirely on the specific constraints of the selection:
📍 Selecting 1 word from each of 3 separate columns
where each column has 300,000 words
Multiply the options:
Results: 2.7 * 10^(16) or 27 quadrillion combinations
📍 Selecting any 2 words from a single list of 300,000 words
with no repetition
Using the combination formula C(n, r)
Results: 4.5 * 10^(10) or 45 billion pairs
📍 Selecting 12 words from a list of 300,000
no repetition, order doesn't matter
Results: Astronomically large number
1.3 * 10^(52) combinations
📍 Creating a 500-word essay from 300,000 words
with repetition allowed
If order matters (permutations)
Results: 300,000^(500), which is ≈10^(2774)
Key Distinction
If you are choosing one item from each distinct category
Multiply the counts
If you are choosing multiple items from a single pool
Use combinations C(n,r) or permutations P(n,r)
which grow exponentially with the size of the pool
300,000 Words
Frontier Model-- What is?
Frequency of Occurrence
The Wastage
Combinatorial Explosion
Where Do We Go From Here?