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.
- (a) 6
- (b) 8
- (c) 10
- (d) 12 ✓ UPSC's answer
Why the answer is (d)
• QUEUE has the letters Q, U, E, U, E.
• Q must be immediately followed by U, so treat "QU" as one block. The items to arrange are then QU, U, E, E.
• Four items with E repeated twice: 4! ÷ 2! = 12 arrangements.
• Every word in which Q is followed by U is counted exactly once, because the two U's are identical. Hence 12: (d).
Why the other options are wrong
- (a) 6
- 6 counts too few; the correct count is 4!/2! = 12.
- (b) 8
- 8 is not obtained by any correct count; the answer is 12.
- (c) 10
- 10 counts too few; the correct count is 4!/2! = 12.
Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2026, held on 24 May 2026. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.