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.
Answer & explanation
Answer: (d) 12
Glue Q and U together as one block 'QU'. Then arrange four units — QU, U, E, E — where the two E's are identical: 4!/2! = 12.
- QUEUE has Q, U, U, E, E.
- Tie Q to a U as a block: the units are QU, U, E, E.
- Arrangements = 4! ÷ 2! (two identical E's) = 24 ÷ 2 = 12.
- Check: Q occurs once, so each word has exactly one block position — no word is counted twice.
Remember · 'X always followed by Y' → treat XY as one block, then divide by factorials of repeated letters.
Question and answer: UPSC's provisional GS Paper II (2026, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). ·