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

Solution (By Examveda Team)

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
$$\eqalign{ & = \frac{{6!}}{{2! \times 2!}} \cr & = \frac{{6 \times 5 \times 4 \times 3 \times 2 \times 1}}{{2 \times 2}} \cr & = 180 \cr} $$