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

Answer: Option C

The given word contains 9 letters, namely 4A, 2L, 1H, 1B and 1D.
∴ Required number of ways
$$\begin{array}{rl}& =\frac{9!}{4!2!1!1!1!}\\ & =\frac{9\times 8\times 7\times 6\times 5\times 4\times 3\times 2\times 1}{4\times 3\times 2\times 1\times 2}\\ & =7560\end{array}$$