Word formation – From the letters E, O, P, R, how many meaningful English words of length 4 can be formed using each letter only once?

Introduction / Context:This item asks for the count of 4-letter dictionary words that can be built from E, O, P, R with no repetition and using all letters. The key skill is to recognize high-frequency anagrams and exclude nonstandard permutations.

Given Data / Assumptions:

• Letter set: {E, O, P, R}.
• Use each letter once; word length 4.
• Words must be standard English.

Concept / Approach:Two clear words are “ROPE” and “PORE.” Both are high-frequency words (rope: cord; pore: to read/study attentively; also a skin opening). Other permutations such as “REOP,” “OPER,” “OEPR” are not accepted as independent words (note: “oper-” exists as a combining form but not as a standalone word in general-purpose dictionaries).

Step-by-Step Solution:Candidates: ROPE (valid), PORE (valid), PROE/REOP/OPER (invalid as standalone standard words).Hence count = 2.

Verification / Alternative check:Check a standard dictionary; “rope” and “pore” are uncontroversially valid. “Repo” (repurchase agreement) exists as a financial noun, but it requires R-E-P-O; our letters can form “REPO,” but many reasoning sets exclude specialized abbreviations/short forms. To remain conservative and consistent with exam conventions, accept “ROPE” and “PORE.”

Why Other Options Are Wrong:

• None/One: Under-count.
• Three/Four: Over-count by including nonstandard or abbreviation-like strings.

Common Pitfalls:Counting “REPO” as a general English word; many tests avoid finance-derived abbreviations. If a test explicitly permits common financial terms, the key would note it; absent that, two is the accepted count.

Final Answer:Two