Dictionary Order Position of 'BARE'
To find the position of the word 'BARE' when all combinations of the letters B, A, R, E are arranged alphabetically, follow these steps:
1. Alphabetical Order of Letters
First, arrange the given letters in alphabetical order:
- A, B, E, R
2. Count Words Starting with Earlier Letters
Identify words that come before 'BARE' in the dictionary.
- Words starting with 'A': The remaining 3 letters (B, E, R) can be arranged in $3!$ ways. $3! = 3 \times 2 \times 1 = 6$ There are 6 words starting with 'A'.
3. Determine Position within 'B' Words
Now, consider words starting with 'B'. The target word is 'BARE'.
- Words starting with 'BA': The second letter is 'A'. The remaining letters are E, R.
List the arrangements of E, R alphabetically:
- BAER (This is the 1st word starting with 'BA')
- BARE (This is the 2nd word starting with 'BA')
4. Calculate Total Position
The total position of 'BARE' is the sum of words starting with earlier letters plus its position among the words starting with 'B'.
- Position = (Words starting with 'A') + (Position of 'BARE' among words starting with 'BA')
- Position = $6 + 2 = 8$
Therefore, 'BARE' is at the $8^{\text{th}}$ position.
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