In a dictionary, the words are arranged in an alphabetical order.
(i) Starting with A, the remaining 4 letters G, A, I, N can be arranged in 4! = 24 ways. These are the first 24 words.
(ii) Then, starting with G, the remaining letters A, A, I, N can be arranged in \(\frac{4!}{2!}\) = 12 ways. Thus, there are 12 words starting will G.
(iii) Now, the words will start with I. Starting with I, the remaining letters A, G, A, N can be arranged in \(\frac{4!}{2!}\) = 12 ways. So, there are 12 words, which start with I.
(iv) Thus, so far, we have constructed 24 + 12 + 12, i.e., 48 words. The 49th word will start with N and is NAAGI. Hence, the 50th word is NAAIG.
