Find the number of permutations of the letters in the word: philadelphia

There are 12 letters in P H I L A D E L P H  I A AND THERE AE:
2 P, 2 H, 2 A, 2 I

Permutation of ¹²P₁₂ = 12! , but mind you there are repeated letters so 
the final Permutation: 12!/(2!)(2!)(2!)(2!) = 29 937 600 ways of arranging letters

The first one is 2/3the second is 1/160the third is 4/125