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QUESTION

CSAT

Medium

Maths

Prelims 2026

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.

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Explanation

Answer: D — 12

We need arrangements of the letters of QUEUE (one Q, two U's, two E's) such that Q is immediately followed by U.

Glue Q to a U.

Treat "QU" as a single block. The remaining letters are one UU and two EE's. So we are arranging four objects: {QU,U,E,E}\{QU, U, E, E\}.

Count arrangements with the repeated EE.

4!2!=242=12\frac{4!}{2!} = \frac{24}{2} = 12

(The two EE's are identical; the UU inside the QU-block is distinguishable from the lone UU by the constraint that one is preceded by Q and the other isn't.)

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