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

Answer: Option D

The given word contains 9 letters, all different.
∴ Required number of ways
$$\begin{array}{rl}& ={}^9{P}_9\\ & =9!\\ & =\left(9\times 8\times 7\times 6\times 5\times 4\times 3\times 2\times 1\right)\\ & =362880\end{array}$$