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 2520

The given word contains 7 letters out of which E is taken 2 times and all other letters are different .
∴ Required number of ways
$$\eqalign{ & = \frac{{7!}}{{2!}} \cr & = \frac{{7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1}}{2} \cr & = 2520 \cr} $$
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