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

Solution (By Examveda Team)

The given words contains 8 letters out of which U is taken 2 times and all other letters are different.
∴ Required number of ways
$$\eqalign{ & = \frac{{8!}}{{2!}} \cr & = \frac{{8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1}}{2} \cr & = 20160 \cr} $$