Question

If all the words, with or without meaning, are written using the letters of the word QUEEN and are arranged as in English dictionary, then the position of the word QUEEN is :

• A. \(44^{\mathrm{th}}\)
• B. \(45^{\mathrm{th}}\)
• C. \(46^{\mathrm{th}}\)
• D. \(47^{\mathrm{th}}\)

Hint:

Arrange letters alphabetically as E, E, N, Q, U and count words that come before QUEEN letter by letter.

Answer 1

The Correct Option is C

Alphabetical order of the letters: E, E, N, Q, U.
Words starting with E: remaining Q, U, E, N (all distinct) give \(4! = 24\).
Words starting with N: remaining Q, U, E, E give \(\frac{4!}{2!} = 12\).
Words starting with Q: second letter in order E, N, U.
QE _ _ _: remaining U, N, E gives \(3! = 6\).
QN _ _ _: remaining U, E, E gives \(\frac{3!}{2!} = 3\).
QU _ _ _: remaining E, E, N; the first word in order is QUEEN itself.
Words before QUEEN = \(24 + 12 + 6 + 3 = 45\), so its position is 46.
Answer: (3) \(46^{\mathrm{th}}\)