Question

The maximum number of different permutations of 4 letters of the word EARTHQUAKE is

a)2910. b)2550. c)2190. d)2091

Answer 1

there are 8 letters in which 2 are repeated
Case 1
4 distinct letters Permutation = 8C4 × 4!
Case 2
2 same 2 distinct lettersPermutation = 2C1 × 7C2 × 4!
Case 3
2 same & 2 same letters Permutation = 4! / 2!×2!
Total no of ways = case 1+ case 2+ case 3
Answer = 1680 + 510 + 6 = 2190