CUET UG 2025 — General Test Quantitative Reasoning

The word 'RUMOUR' has 6 letters total.

Counting the frequency of each letter:

• R appears 2 times
• U appears 2 times
• M appears 1 time
• O appears 1 time

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The number of different arrangements with repeated letters is given by:

Number of arrangements $= \dfrac{n!}{n_1! \times n_2! \times ...}$=n1​!×n2​!×...n!​

where $n$n is the total number of letters and $n_1, n_2, ...$n1​,n2​,... are the frequencies of each repeating letter.

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Substituting the values:

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

$$= \dfrac{6 \times 5 \times 4 \times 3 \times 2 \times 1}{2 \times 2}$$=2×26×5×4×3×2×1​

$$= \dfrac{720}{4}$$=4720​

$$= 180$$=180

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Therefore, the letters of 'RUMOUR' can be arranged in 180 different ways.