The max no of different permutations of 4 letters of the word EARTHQUAKE

But the answer is 2190...

Case 1 4 distinct lettersPermutation = 8c4 × 4!Case 2 2 same 2 distinct lettersPermutation = 2c1 × 7c2 × 4!Case 32 same & 2 same lettersPermutation = 4! / 2!×2!Total no of ways = case 1+ case 2+ case 3Answer = 1680 + 510 + 6 = 2190

There are 3 different casesCase 14 distinct letters Permutation = 8c4 × 4!Case 2 2 same 2 distinct letters Permutation = 2c1 × 7c2 × 4!Case 32 same & 2 same letters Permutation = 4! / 2!×2!Total no of ways = case 1+ case 2+ case 3Answer = 1680 + 514 + 6 = 2190