In How Many Ways The Letters Of The Word Engineering Ca Be Arranged?

There are 11! Different arrangements of 11 letters. However, the word "engineering" has 3 repetitions of the letters "e" and "n" and two repetitions of the letters "g" and "I". These will reduce the number of distinguishable arrangements by a factor of (3!*3!*2!*2!) = 144.
The number of distinguishable arrangements is 11!/144 = 277,200.