SOLUTION: In how many distinct ways can the word INDEPENDENCE be arranged?

The formula for the number of distinguishable arrangements is:



INDEPENDENCE has 12 letters, so 12! is the numerator.
There are 3 indistinguishable N's, so one of the factors of the denominator is 3!
There are 2 indistinguishable D's, so one of the factors of the denominator is 2!
There are 4 indistinguishable E's, so one of the factors of the denominator is 4!

Answer: 

Edwin