In how many different ways can the letters of the word GOODNESS be arranged?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 10080
The number of arrangements of \(n\) letters in which some letters repeat is \(n!\) divided by the factorial of each repeat, because swapping two identical letters gives no new word.
GOODNESS has 8 letters: O twice, S twice, and G, D, N, E once each
Arrangements \(\displaystyle =\frac{8!}{2!\times2!}=\frac{40320}{4}=10080\)