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

LohaHridoy
  1. 277200
  2. 92400
  3. 69300
  4. 23100
  5. None of these

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AhmedNazir

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Answer: Option 1

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

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