The letters of the word NIGHT are written in all possible ways and these words are arranged as in a dictionary. What is the 50^ th word in this sequence?

Step-by-step solution

First, arrange the letters of the word NIGHT in alphabetical order: G, H, I, N, T. The number of words starting with G is 4! = 24 . The number of words starting with H is 4! = 24 . The total number of words starting with G or H is 24 + 24 = 48 . The 49^ th word will be the first word starting with I. The remaining letters in alphabetical order are G, H, N, T. Thus, the 49^ th word is IGHNT. To find the 50^ th word, we find the next lexicographical permutation by swapping the last two letters. The 50^ th word is IGH