In how many different ways can the letters of the word OPERATE be arranged?
A
64
B
960
C
20160
D
40320
E
None of these
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
$$\eqalign{ & = \frac{{8!}}{{2!}} \cr & = \frac{{8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1}}{2} \cr & = 20160 \cr} $$