Q69·CSAT · Prelims 2026
Permutations — Word Arrangements with Constraints
NumericalPermutation & CombinationArithmetic Problem● Easy
Question
How many words can one form by shuffling the letters of the word QUEUE, if Q is always followed by U?
Options
a
6
b
8
c
10
dAnswer
12
Explanation
The target word is QUEUE, which consists of 5 total letters: one Q, two Us, and two Es .
Apply the structural constraint: The letter Q must always be followed by U. This means we can treat the combination [QU] as a single, indivisible block.
Count the remaining elements to arrange:
The fixed block: [QU] (1 item)
The remaining letters: one U and two Es (3 items)
Total independent items to arrange = 1 + 3 = 4 items.
Calculate Permutations with Repetition: Among these 4 items, the letter E repeats twice. Apply the standard permutation formula for repeating elements:
Total Words = 4!/2! = 24/2 = 12 words
When specific letters must always stay together in a set sequence, bind them into a single block and find the total permutations for the remaining items.
Answer: (d).
Question details
Year
2026
Paper
CSAT
Question
Q69
Section
Quantitative Aptitude
Sub-topic
Permutation & Combination
Type
Arithmetic Problem
Difficulty
Easy
Source hint
Combinatorics — string block permutation rules
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