Constrained word formation – From the letters of TEAR, how many meaningful 3-letter English words can be formed that begin with “A” (no letter repetition within a word)?

Introduction / Context:
Here we must form 3-letter words that begin specifically with “A” using letters from TEAR, with no letter used more than once in a word. Such constraints reduce the search space and emphasize recall of common short words.

Given Data / Assumptions:

• Available letters: {T, E, A, R}.
• Words must start with A and be 3 letters long.
• No letter repetition in a single word.

Concept / Approach:
Build “A _ _” using the remaining letters {T, E, R}. Three standard words result: “ATE,” “ARE,” and “ART.” Each is extremely common in everyday usage, satisfies the starting-letter constraint, and uses no letter twice.

Step-by-Step Solution:
A + T/E/R → “ATE,” “ARE,” “ART.”Verify all three are standard words: ATE (past tense of eat); ARE (present of be, plural/second person); ART (skill; also archaic “thou art”).Total = 3.

Verification / Alternative check:
These words are listed in all major dictionaries. “ARE” and “ART” are especially frequent in exams due to their short length and grammatical functions.

Why Other Options Are Wrong:

• One/Two: Under-count; at least three valid words exist.
• Four/Five: Over-count; no additional distinct, non-repeating 3-letter words beginning with A can be made from TEAR.

Common Pitfalls:
Overlooking functional words such as “ARE” because they are grammatical rather than lexical nouns/verbs only. Exam conventions include such forms.

Final Answer:
Three