In how many different ways can the letters of the word ENGINEERING be arranged?
A
277200
B
92400
C
69300
D
23100
E
None of these
Correct Answer: 277200
The given word contains 11 letters, namely 3E, 3N, 2G, 2I and 1RSo, Required number of ways :
$$\eqalign{ & = \frac{{11!}}{{3! \,3! \,2! \,2! \,1!}} \cr & = \frac{{11 \times 10 \times 9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1}}{{6 \times 6 \times 2 \times 2 \times 1}} \cr & = \left( {11 \times 10 \times 9 \times 8 \times 7 \times 5} \right) \cr & = 277200 \cr} $$
