Arrange the following words in the sequence in which they occur in the dictionary: 1. Ball 2. Balanced 3. Balls 4. Balance 5. Balancing

Introduction / Context:
This dictionary order question uses five words that all begin with the letters “Bal-”: Ball, Balanced, Balls, Balance and Balancing. Because the words share a long prefix, you must carefully compare letters beyond it and use the rule that a shorter word preceding a longer extension comes first.

Given Data / Assumptions:
- Words with indices:
1. Ball
2. Balanced
3. Balls
4. Balance
5. Balancing
- Standard English alphabetical rules apply.

Concept / Approach:
Since all words start with “bal”, you next compare the fourth letter. Some words have “bala…” while others have “ball…”. The “bala…” words come before the “ball…” words because a comes before l. Among the “bala…” words, you then compare letters where they differ, and if one is a complete prefix of another, the shorter one is earlier in the dictionary.

Step-by-Step Solution:
Step 1: Consider the fourth letter of each word: Ball → b a l l Balanced → b a l a… Balls → b a l l s Balance → b a l a n c e Balancing → b a l a n c i n g Step 2: Words with “bala…” (indices 2, 4, 5) come before words with “ball…” (indices 1, 3) because a < l at the fourth position. Step 3: Order the “bala…” group: Balance (4), Balanced (2), Balancing (5). Compare Balance vs Balanced: they match as “balance” vs “balanced”. The shorter word Balance ends first, so it comes before Balanced. Now compare Balanced vs Balancing: both share “balanc” and then have “ed” vs “ing”. At the next differing letter, e comes before i, so Balanced (2) comes before Balancing (5). Step 4: Order the “ball…” words: Ball (1) vs Balls (3). Ball is a complete prefix of Balls, so Ball comes before Balls. Step 5: Combine all: Balance (4), Balanced (2), Balancing (5), Ball (1), Balls (3) → 4,2,5,1,3.

Verification / Alternative check:
Simulate dictionary scanning: all “balance…” words come before “ball…” words. Under “balance…”, you see “balance” first, then “balanced”, then “balancing”. Only after exhausting these do you see “ball”, then “balls”. This sequence exactly matches 42513.

Why Other Options Are Wrong:
- 24135 puts Balanced before Balance, contrary to the prefix rule.
- 42135 incorrectly places Balancing after Ball, even though all “bala…” words must precede any “ball…” words.
- 54213 has Balancing first, ignoring that words beginning “bala…” must be ordered correctly among themselves and appear before “ball…”.

Common Pitfalls:
A frequent mistake is to treat Ball as if it should come earliest because it is very short and familiar. However, dictionary ordering is based on letter sequence, not word length alone. Within “bala…” and “ball…”, word length becomes relevant only once all earlier letters match exactly. Always check the exact positions where words diverge.

Final Answer:
The correct dictionary order is Balance, Balanced, Balancing, Ball, Balls, corresponding to 42513.