Analyzing the Letters of the Word DISTRIBUTION

The question asks us to identify the word that cannot be formed using only the letters available in the word DISTRIBUTION. To solve this type of word formation problem, we first need to list all the letters present in the given word and count how many times each letter appears.

Let's break down the word DISTRIBUTION:

• D: 1 time
• I: 2 times
• S: 1 time
• T: 2 times
• R: 1 time
• B: 1 time
• U: 1 time
• O: 1 time
• N: 1 time

So, the available letters and their counts are: D(1), I(2), S(1), T(2), R(1), B(1), U(1), O(1), N(1). We need to check each option word against this list. A word can be formed if all its letters are present in DISTRIBUTION and are not used more times than they appear in DISTRIBUTION.

Checking Each Option Word

Option 1: BUTTON

Let's examine the letters in the word BUTTON:

• B: 1 time
• U: 1 time
• T: 2 times
• O: 1 time
• N: 1 time

Comparing these letters to the letters available in DISTRIBUTION:

• B: Needs 1, Available 1 - Yes
• U: Needs 1, Available 1 - Yes
• T: Needs 2, Available 2 - Yes
• O: Needs 1, Available 1 - Yes
• N: Needs 1, Available 1 - Yes

All the letters required for BUTTON are available in DISTRIBUTION with sufficient counts. So, BUTTON can be formed.

Option 2: DISTURB

Let's examine the letters in the word DISTURB:

• D: 1 time
• I: 1 time
• S: 1 time
• T: 1 time
• U: 1 time
• R: 1 time
• B: 1 time

Comparing these letters to the letters available in DISTRIBUTION:

• D: Needs 1, Available 1 - Yes
• I: Needs 1, Available 2 - Yes
• S: Needs 1, Available 1 - Yes
• T: Needs 1, Available 2 - Yes
• U: Needs 1, Available 1 - Yes
• R: Needs 1, Available 1 - Yes
• B: Needs 1, Available 1 - Yes

All the letters required for DISTURB are available in DISTRIBUTION with sufficient counts. So, DISTURB can be formed.

Option 3: BRITAIN

Let's examine the letters in the word BRITAIN:

• B: 1 time
• R: 1 time
• I: 2 times
• T: 1 time
• A: 1 time
• N: 1 time

Comparing these letters to the letters available in DISTRIBUTION:

• B: Needs 1, Available 1 - Yes
• R: Needs 1, Available 1 - Yes
• I: Needs 2, Available 2 - Yes
• T: Needs 1, Available 2 - Yes
• A: Needs 1, Available 0 - No
• N: Needs 1, Available 1 - Yes

The word BRITAIN requires the letter 'A'. However, the letter 'A' does not appear anywhere in the word DISTRIBUTION. Therefore, the word BRITAIN cannot be formed using the letters of DISTRIBUTION.

Option 4: BURNT

Let's examine the letters in the word BURNT:

• B: 1 time
• U: 1 time
• R: 1 time
• N: 1 time
• T: 1 time

Comparing these letters to the letters available in DISTRIBUTION:

• B: Needs 1, Available 1 - Yes
• U: Needs 1, Available 1 - Yes
• R: Needs 1, Available 1 - Yes
• N: Needs 1, Available 1 - Yes
• T: Needs 1, Available 2 - Yes

All the letters required for BURNT are available in DISTRIBUTION with sufficient counts. So, BURNT can be formed.

Conclusion

Based on the analysis of each option, the word that cannot be formed using the letters of DISTRIBUTION is BRITAIN because it contains the letter 'A', which is not present in the original word.

Revision Table: Word Formation Rules

Additional Information on Word Formation from Letters

Word formation questions are common in various aptitude and reasoning tests. They check your observation skills and vocabulary. Here are a few related points:

• Anagrams: These are words formed by rearranging all the letters of another word exactly once. This is a specific type of word formation where all letters must be used.
• Subsets: The words formed in questions like the one above are subsets of the letters of the main word. You use some or all of the letters, respecting their frequency.
• Letter Frequency: Quickly counting the frequency of each letter in the original word is a crucial first step to efficiently check options.

Practicing with different words can help improve your speed and accuracy in solving these letter-based problems. Always remember to carefully compare the required letters for each option against the available letters and their counts in the source word.