Word-formation count: Using each letter only once, how many meaningful English words can be formed from the letters L, E, G, U?

Introduction / Context:This question tests your ability to form valid English words from a fixed multiset of letters, with the constraint that each letter may be used at most once per word. The letter bag is L, E, G, U (one of each). The task is to count how many distinct, common-dictionary words you can make under these rules.

Given Data / Assumptions:

• Available letters: {L, E, G, U}.
• Each letter can be used once per word.
• We count standard English words that appear in common dictionaries (no proper nouns, abbreviations, or rare technical forms).

Concept / Approach:Enumerate plausible permutations that could yield everyday words. A practical strategy is to consider likely onsets (GL-, L-, G-) and check common endings (-UE, -UE, -UG, etc.). Two familiar words emerge quickly: GLUE and LUGE. Both use all four letters exactly once and are common in everyday English: “glue” (noun/verb) and “luge” (winter sliding sport). No other common permutations (e.g., GULE, EGUL, ULEG) yield standard words in general-purpose usage.

Step-by-Step Solution:1) List permutations with GL-: GLUE ✓.2) List permutations with L-: LUGE ✓.3) Reject non-words like GULE (archaic/rare), EGUL, ULEG.4) Count valid everyday words: 2.

Verification / Alternative check:Cross-check in a standard learner’s dictionary: both “glue” and “luge” are attested, common entries. Other sequences do not appear as standalone everyday words, ensuring the count remains two.

Why Other Options Are Wrong:

• None / One: Under-count; both GLUE and LUGE are valid.
• Three: Over-count; no third common word from these exact letters.

Common Pitfalls:Including rare or archaic forms, proper nouns, or misspellings. The question intends everyday vocabulary, where exactly two words fit.

Final Answer:Two