Constrainted word formation – From the letters A, L, E, P, how many meaningful 4-letter English words can be formed that begin with “P” (use each letter at most once, no repetition)?

Introduction / Context:This alphabet-test variant adds an extra constraint: the valid words must begin with a specific letter. We are given letters A, L, E, P and must count how many 4-letter meaningful English words start with “P,” using available letters without repeating any letter.

Given Data / Assumptions:

• Letters available: A, L, E, P.
• Word length = 4; begin with “P.”
• No letter repetition.

Concept / Approach:Construct “P _ _ _” using remaining letters {A, L, E} in some order. The well-known valid words are “PALE,” “PEAL,” and “PLEA.” All three are standard English words: PALE (light color; lacking color), PEAL (a loud ringing of bells), PLEA (request; legal assertion). No other distinct 4-letter arrangement starting with P and using A/L/E exactly once yields additional standard words beyond these three.

Step-by-Step Solution:Enumerate: PALE, PELA (no), PEAL, PELA (dup/nonstandard), PLEA.Confirm dictionary status for PALE, PEAL, PLEA.Count = 3.

Verification / Alternative check:Cross-check via a trusted dictionary or word list; all three appear commonly and are frequently used in exams of this type.

Why Other Options Are Wrong:

• One/Two: Under-count; ignore one or more of the valid triplet.
• Four/Five: Over-count; would require accepting nonstandard or duplicated arrangements.

Common Pitfalls:Overlooking “PLEA,” which is very common in legal and general contexts. Always verify each candidate begins with P and uses letters without repetition.

Final Answer:Three