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

Answer: Option A

The given word contains 11 letters, namely 3E, 3N, 2G, 2I and 1R
So, Required number of ways :
$$\begin{array}{rl}& =\frac{11!}{3!3!2!2!1!}\\ & =\frac{11\times 10\times 9\times 8\times 7\times 6\times 5\times 4\times 3\times 2\times 1}{6\times 6\times 2\times 2\times 1}\\ & =\left(11\times 10\times 9\times 8\times 7\times 5\right)\\ & =277200\end{array}$$