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UPSC Prelims 2026 CSAT, question 9

Topic: Counting and probability

Q9

How many words can one form by shuffling the letters of the word QUEUE, if Q is always followed by U? The words thus formed need not necessarily have any meaning.

  1. (a) 6
  2. (b) 8
  3. (c) 10
  4. (d) 12Correct answer

Solution.

Answer: (d) 12

  1. The word QUEUE has 5 letters: one Q, two U's, and two E's.
  2. Since Q must always be immediately followed by U, bind Q and the U immediately following it into a single unit (QU), leaving four items to arrange: (QU), U, E, and E.
  3. Because the two E's are identical and (QU) is distinct from the remaining U, the number of distinct arrangements is 4!2!=242=12\frac{4!}{2!} = \frac{24}{2} = 12.

Trap: Do not divide by 2!2! for the U's: one U sits inside the QU block and the other stands alone, so they are not interchangeable.