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

Solution (By Examveda Team)

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