If the letters of the word SMART are permuted and all possible words so formed are arranged as in a dictionary with serial numbers, then the 89^ th word is

Step-by-step solution

The letters of the word SMART in alphabetical order are A, M, R, S, T. Number of words starting with A = 4! = 24 Number of words starting with M = 4! = 24 Number of words starting with R = 4! = 24 Total words so far = 24 + 24 + 24 = 72 The 89^ th word must start with S. The remaining letters are A, M, R, T. Number of words starting with SA = 3! = 6 (Total = 78 ) Number of words starting with SM = 3! = 6 (Total = 84 ) The 89^ th word must start with SR. The remaining letters are A, M, T. Number of words starting wit