In how many different ways can the letters of the word 'RUMOUR' be arranged?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 180
\(n\) different letters can be arranged in \(n!\) ways. When some letters repeat, swapping two identical letters gives the same word, so the count is divided by the factorial of each repeat: \(\frac{n!}{p!\,q!}\).
RUMOUR has 6 letters: R twice, U twice, M and O once each
Arrangements \(\displaystyle =\frac{6!}{2!\times2!}=\frac{720}{4}=180\)
The value 720 in Option (1) is \(6!\), which counts the two R’s and the two U’s as different letters.