Word formation – From the letters A, E, R, how many meaningful 3-letter English words can be formed using each letter exactly once?

Introduction / Context:This is a classic short-anagram question. With the letters A, E, R, we need to count all 3-letter standard English words that use each letter once. These items test recognition of common function words as well as content words.

Given Data / Assumptions:

• Letters available: {A, E, R}.
• Word length exactly 3; no repetition.
• Accept standard dictionary words, including common function words.

Concept / Approach:Enumerate plausible combinations. The well-known valid words are “ARE,” “EAR,” and “ERA.” All three appear widely in print: “are” (form of the verb be), “ear” (organ of hearing), and “era” (period of time). Because each uses all three letters once, the total count is three.

Step-by-Step Solution:Try each starting letter: A__ → ARE; E__ → EAR; R__ → ERA.Verify dictionary status for all three.Therefore, total meaningful words = 3.

Verification / Alternative check:Cross-check with a reliable dictionary list. These words are elementary-level entries and commonly used in reasoning tests specifically because they are unambiguous and frequent.

Why Other Options Are Wrong:

• None/One/Two: Under-count the valid set.

Common Pitfalls:Overlooking function words like “are” due to focusing only on nouns. Short word problems often hinge on including these.

Final Answer:Three