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Step-by-Step Solution
Step 1: Identify the Given Letters
The word "QUEEN" consists of the letters Q, U, E, E, N. Notice there are 5 letters in total, with "E" repeated twice.
Step 2: Arrange Letters in Alphabetical Order
In alphabetical order, the letters are E, E, N, Q, U. We need to find how many words (with or without meaning) come before "QUEEN" when all permutations are listed in dictionary order.
Step 3: Count Words Beginning with Letters That Come Before Q
Words starting with E:
If the first letter is E, the remaining letters are Q, U, E, N (one E has already been used). There are 4 letters left with one repetition (E). Thus, the number of permutations is
$ \frac{4!}{1!} = 24 $.
Words starting with N:
If the first letter is N, the remaining letters are Q, U, E, E. Here, E is repeated twice. Thus, the number of permutations is
$ \frac{4!}{2!} = 12 $.
Total words so far = 24 (E...) + 12 (N...) = 36.
Step 4: Count Words Starting with Q but Second Letter Comes Before U
Now consider words starting with Q. The remaining letters to arrange are U, E, E, N. In alphabetical order, these are E, E, N, U.
Second letter = E:
Remaining letters are U, E, N. Since there is only one repeated E, the number of permutations is
$ \frac{3!}{1!} = 6 $.
Second letter = N:
Remaining letters are U, E, E. Here E is repeated twice. Thus, the number of permutations is
$ \frac{3!}{2!} = 3 $.
Total for Q as the first letter but with second letter before U = 6 + 3 = 9.
Step 5: Sum Up All Earlier Count
Add up all the permutations that come before words starting with "QU":
24 (for E...) + 12 (for N...) + 9 (for QE..., QN...) = 45.
Step 6: Position of "QUEEN"
The next word (after those 45) is "QUEEN", so its position is the 46th.
Answer: 46th
