Arrange the following words in correct dictionary order and then select the option that shows their sequence: 1. DIRECTION 2. DIRECTED 3. DIRECTOR 4. DIRECTING.

Introduction / Context:
This problem tests your understanding of dictionary or alphabetical order using four closely related words. Because all words share a common root, learners must carefully compare letters at different positions to determine the correct order. You are given the words DIRECTION, DIRECTED, DIRECTOR, and DIRECTING and asked to identify their proper sequence as they would appear in an English dictionary.

Given Data / Assumptions:

• Indexed words: 1. DIRECTION, 2. DIRECTED, 3. DIRECTOR, 4. DIRECTING.
• All words begin with the prefix DIRECT, so sorting will depend on letters that come after this shared prefix.
• We follow standard dictionary ordering rules and compare letters from left to right.
• Each answer choice provides a possible ordering of the indices.

Concept / Approach:
When multiple words share an identical starting sequence, dictionary order is determined by the first position where they differ. Here, DIRECTION, DIRECTED, DIRECTOR, and DIRECTING all start with DIRECT. After this prefix, letters appear as E, I, I, and I respectively. One must continue comparing letters until a difference appears. The goal is to find the exact sequence in which these four words would be listed by a dictionary and then match that sequence with the correct option.

Step-by-Step Solution:
Step 1: Write the words clearly: DIRECTED, DIRECTING, DIRECTION, DIRECTOR.Step 2: After the common prefix DIRECT, the remaining parts are: ED, ING, ION, OR.Step 3: Compare DIRECTED and the others. Since the next letter after DIRECT is E in DIRECTED and I in the other three, DIRECTED comes first because E comes before I.Step 4: Now consider DIRECTING, DIRECTION, and DIRECTOR. They all have DIRECTI as a prefix. After DIRECTI, the letters are N, O, and O respectively.Step 5: DIRECTING has N immediately after DIRECTI, while DIRECTION and DIRECTOR have O after DIRECTI. Because N comes before O, DIRECTING comes second overall.Step 6: Compare DIRECTION and DIRECTOR. Up to DIRECTO, they match. Next letters are N in DIRECTION and R in DIRECTOR. Since N comes before R, DIRECTION is third and DIRECTOR is fourth.Step 7: Thus, dictionary order is: DIRECTED (2), DIRECTING (4), DIRECTION (1), DIRECTOR (3). The sequence of indices is 2, 4, 1, 3.

Verification / Alternative check:
A quick check is to think of how you would look for these words in a dictionary that has entries like DIRECT, DIRECTED, DIRECTING, DIRECTION, DIRECTOR. Common experience suggests that verb forms in ED and ING often appear before nouns like DIRECTION and DIRECTOR. Confirming the letter by letter comparison ensures that this intuition is correct. Checking that no other ordering option matches this pattern confirms that the correct sequence of indices is 2, 4, 1, 3.

Why Other Options Are Wrong:
Option 1, 4, 3, 2 is wrong because it places DIRECTION before DIRECTED, even though the letter E after DIRECT in DIRECTED comes before I in DIRECTION.Option 4, 2, 3, 1 is wrong because it begins with DIRECTING instead of DIRECTED, which contradicts the E before I rule.Option 4, 1, 2, 3 is also incorrect because it misplaces DIRECTING and DIRECTED relative to one another and does not follow the proper alphabetical comparisons.

Common Pitfalls:
Students often pay attention only to the first few letters and forget to compare beyond the shared prefix. Another pitfall is relying on meaning instead of strict alphabetic rules, for example thinking that DIRECTION should follow DIRECTOR based on real world associations. Always compare words letter by letter, ignoring meaning, to avoid such errors. Writing out the words and underlining the first differing letter helps maintain accuracy in these problems.

Final Answer:
The correct dictionary order corresponds to the index sequence 2, 4, 1, 3.