In how many different ways can the letters of the word RUMOUR be arranged?

Answer: Option C

The given word contains 6 letter out of which R is taken 2 times, U is taken to 2 times and other letters are all different.
∴ Required number of ways
$$\begin{array}{rl}& =\frac{6!}{2!\times 2!}\\ & =\frac{6\times 5\times 4\times 3\times 2\times 1}{2\times 2}\\ & =180\end{array}$$