CUET UG 2025 — General Test Quantitative Reasoning

The word GOODNESS has 8 letters total.

Writing out each letter: G - O - O - D - N - E - S - S

Counting each letter:

• G appears 1 time
• O appears 2 times
• D appears 1 time
• N appears 1 time
• E appears 1 time
• S appears 2 times

O repeats 2 times and S repeats 2 times.

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When letters repeat, the formula is:

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​,... represent how many times each letter repeats.

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Number of arrangements $= \dfrac{8!}{2! \times 2!}$=2!×2!8!​

$$8! = 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1$$8!=8×7×6×5×4×3×2×1

$$8! = 40,320$$8!=40,320

$$2! = 2$$2!=2

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Number of arrangements $= \dfrac{40,320}{2 \times 2}$=2×240,320​

$$= \dfrac{40,320}{4}$$=440,320​

$$= 10,080$$=10,080

Therefore, the letters of GOODNESS can be arranged in 10,080 different ways.