Word formation – Using all letters N, R, E, A exactly once, how many meaningful 4-letter English words can be made?

Introduction / Context:Another anagram count: with N, R, E, A, determine the number of standard 4-letter words using all letters exactly once. Such items reward systematic enumeration and knowledge of common vocabulary forms.

Given Data / Assumptions:

• Letters: {N, R, E, A}.
• Use all four letters; no repeats.
• Only mainstream dictionary words are accepted.

Concept / Approach:Two very common words are “NEAR” and “EARN.” Many other permutations do not stand as independent standard words (e.g., “RENA,” “RANE” as general English). Therefore, a conservative and widely accepted count is two.

Step-by-Step Solution:Check candidates: NEAR (valid), EARN (valid).Other permutations like NARE/REAN/ERNA are not accepted mainstream English words.Hence the total is 2.

Verification / Alternative check:Standard dictionaries and common exam keys agree on NEAR and EARN. These two are frequently chosen as the canonical answers for this letter set.

Why Other Options Are Wrong:

• None/One: Under-count.
• Three/Four: Over-count by including nonwords or names.

Common Pitfalls:Treating proper nouns as valid or assuming any rearrangement becomes acceptable. Reasoning tests prioritize core dictionary entries.

Final Answer:Two