Question: A natural language processing model processes a sentence by selecting 5 distinct words from a vocabulary of 12 words: 5 nouns, 4 verbs, and 3 adjectives. How many ways can the selection include exactly 2 nouns, at least 1 verb, and at least 1 adjective? - Deep Underground Poetry

Understanding the Context

Why This Question Is Resonating Now

Across digital platforms and professional circles, professionals are exploring the nuances of natural language processing (NLP) in practical, scalable ways. The growing demand for accurate, context-aware language models has spotlighted foundational design choices—like how word categories and counts affect sentence diversity and clarity. This specific query—identifying valid splits between nouns, verbs, and adjectives—reveals user curiosity about NLP architecture and linguistic constraints. It’s not just academic; understanding these parameters helps developers, educators, and end users anticipate output credibility and usability.

Social media trends, AI literacy initiatives, and workplace training modules all drive this interest, especially among STEM professionals, linguists, and content strategists navigating the evolving digital ecosystem. The combination of structured word categories with precise selection rules (exactly two nouns, one or more verbs, one or more adjectives) creates a testable framework that matters beyond isolated curiosity.

Key Insights

How to Calculate the Valid Word Combinations

To determine how many ways a sentence can be formed under the constraints—exactly 2 nouns, at least 1 verb, and at least 1 adjective—we apply combinatorics with intentional focus on real-world application. This approach remains neutral, educational, and perfectly suited for platforms like Discover, where depth supports discovery.

We start with fixed counts:

• 2 nouns from 5 available: C(5,2)
• 1 or more verbs from 4: sum over k=1 to 4 (C(4,k))
• 1 or more adjectives from 3: sum over m=1 to 3 (C(3,m))
• Total 5 distinct words: sum across combinations where total selected words = 5, meeting all conditions

We calculate each valid split:

Step 1: Choose 2 nouns from 5

C(5,2) = 10

Final Thoughts

Step 2: Distribute remaining 3 words between verbs and adjectives, with at least 1 each

Valid (verb, adjective) pairs summing to 3 with both ≥1:

• (1 verb, 2 adjectives)
• (2 verbs, 1 adjective)
• (3 verbs, 0 adjectives) → Invalid (must have ≥1 adjective)
• (0 verbs, 3 adjectives) → Invalid (must have ≥1 verb)

So only two viable splits: (1V,2A) and (2V,1A)

Compute combinations:

• (1 verb, 2 adjectives): C(4,1) × C(3,2) = 4 × 3 = 12
• (2 verbs, 1 adjective): C(4,2) × C(3,1) = 6 × 3 = 18

Total verb-adjective combinations = 12 + 18 = 30