CUET UG 2025 — General Test Quantitative Reasoning

The word ASSOCIATION has 11 letters.

Vowels: A, A, O, O, I, I (6 vowels total)

Consonants: S, S, C, T, N (5 consonants total)

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Treat all vowels as one single block since they must stay together.

Items to arrange:

• 1 vowel block (AAOOII)
• 5 consonants (S, S, C, T, N)

Total items = 6

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Arranging these 6 items where S repeats 2 times:

Number of arrangements $= \dfrac{6!}{2!}$=2!6!​

$$= \dfrac{720}{2}$$=2720​

$$= 360$$=360

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Arranging the vowels within their block:

The vowel block contains: A, A, O, O, I, I (6 vowels)

Where A repeats 2 times, O repeats 2 times, and I repeats 2 times:

Number of arrangements $= \dfrac{6!}{2! \times 2! \times 2!}$=2!×2!×2!6!​

$$= \dfrac{720}{2 \times 2 \times 2}$$=2×2×2720​

$$= \dfrac{720}{8}$$=8720​

$$= 90$$=90

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Total arrangements $= 360 \times 90$=360×90

$$= 32,400$$=32,400