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

In how many different ways can the letters of the word OPERATE be arranged? Correct Answer 20160

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

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