From the given alternative words, select the single word that cannot be formed using the letters of the word LEGIBILITY.

Introduction / Context:
This is a classic letter formation problem where you must decide which word cannot be formed from the letters of a given base word. The base word here is LEGIBILITY. Each option uses some subset of its letters. Your task is to determine which option requires at least one letter that is missing or requires a letter more times than it appears in LEGIBILITY.

Given Data / Assumptions:

• Base word: LEGIBILITY.
• Letters and frequencies: L(2), E(1), G(1), I(3), B(1), T(1), Y(1).
• Option A: BILL.
• Option B: ABILITY.
• Option C: BIG.
• Option D: LEG.
• Assumption: Only the letters from LEGIBILITY may be used, and each letter can be used at most as often as it appears in the base word.

Concept / Approach:
The approach is to count all letters in the base word once and then examine each option in turn. If an option uses a letter that does not appear in the base word, or uses a letter too many times, that option cannot be formed. Exactly one option is expected to fail this test. The key is to be systematic and not overlook missing letters like A, which do not appear in LEGIBILITY at all.

Step-by-Step Solution:
Step 1: Record frequencies in LEGIBILITY: L(2), E(1), G(1), I(3), B(1), T(1), Y(1).Step 2: Check BILL: letters B, I, L, L. Required counts are B(1), I(1), L(2). All of these exist with sufficient frequency, so BILL can be formed.Step 3: Check BIG: letters B, I, G. Each of B, I, and G appears in the base word and each only once in the option. So BIG can be formed.Step 4: Check LEG: letters L, E, G. All three letters are present in LEGIBILITY and the required counts are within the available frequencies. So LEG can also be formed.Step 5: Check ABILITY: letters A, B, I, L, I, T, Y. The letter A does not appear anywhere in LEGIBILITY. Therefore, ABILITY cannot be formed from the base word.

Verification / Alternative check:
A quick alternative check is to scan the base word visually and note which letters are present. You will see L, E, G, I, B, T, Y, but no A. Therefore, any option containing A must be invalid. Among the options, only ABILITY includes A, so this confirms that ABILITY cannot be formed. For completeness, you can also confirm that BILL, BIG, and LEG do not introduce new letters and do not overuse any letter beyond its available count.

Why Other Options Are Wrong:
BILL is not the correct answer because it uses only B, I, and L, and all of these letters are present in LEGIBILITY with adequate frequency.BIG is not the correct answer since B, I, and G are all contained in the base word and only used once.LEG is not the correct answer because L, E, and G are clearly present in the base word and are not overused.

Common Pitfalls:
One frequent mistake is to assume that if most letters match, the word is formable, without checking every letter. Letters like A that are completely absent from the base word are easy to miss. Another pitfall is to forget that repeated letters must not exceed the available count in the base word. Systematic letter counting and a quick scan for completely new letters help avoid these errors.

Final Answer:
The word that cannot be formed using the letters of LEGIBILITY is ABILITY.