Word formation – Using the letters K, E, A, B exactly once in each word, how many meaningful 4-letter English words can be formed?

Introduction / Context:We must count dictionary-valid 4-letter words formed from K, E, A, B, with each letter used once per word. Such items blend permutation awareness with vocabulary knowledge. A systematic scan of plausible letter orders is the best approach.

Given Data / Assumptions:

• Letters: {K, E, A, B}.
• All four letters must be used exactly once.
• Only standard English words are allowed.

Concept / Approach:Two well-known words arise: “BEAK” and “BAKE.” Both are common (beak = bird’s bill; bake = cook by dry heat). Attempts like “KEAB,” “KABE,” “AEKB,” etc. do not produce accepted standalone words. Therefore, the correct count is two.

Step-by-Step Solution:List candidates: BEAK (valid), BAKE (valid), KA BE (no), KEBA (no), EBAK (no), etc.Validate via standard dictionary senses.Total valid words = 2.

Verification / Alternative check:General-purpose dictionaries confirm “beak” and “bake.” No other accepted 4-letter words from this specific set exist without repetition or letter omission.

Why Other Options Are Wrong:

• One: Under-count (misses either BAKE or BEAK).
• Three/Four/Five: Over-count by attempting nonwords or variants not recognized in dictionaries.

Common Pitfalls:Accepting abbreviations or proper names as words; these are typically not counted in such tests. Be precise about the “all four letters, once” rule.

Final Answer:Two