If all the permutations of the letters of the word MATRIX are arranged in a dictionary, then what is the 500^ th word?

Step-by-step solution

The letters of the word MATRIX in alphabetical order are A, I, M, R, T, X . Number of words starting with A = 5! = 120 Number of words starting with I = 5! = 120 Number of words starting with M = 5! = 120 Number of words starting with R = 5! = 120 Total words so far = 480 . The 500^ th word must start with T . We need the 20^ th word starting with T . Since the number of words starting with TA is 4! = 24 , the 500^ th word starts with TA . Number of words starting with TAI = 3! = 6 Number of words starting with TAM