If all permutations of the letters of the word $$AGAIN$$   are arranged as in dictionary, then fiftieth word is

Solution :
Starting with the letter $$A$$ and arranging the other four letters, there are $$4! = 24$$  words. These are the first 24 words. Then starting with $$G$$ and arranging $$A, A, I$$  and $$N$$ in different ways, there are $$\frac{{4!}}{{2!1!1!}} = \frac{{24}}{2} = 12{\text{ words}}{\text{.}}$$
Hence, total 36 words.
Next, the $$37^{th}$$ word starts with $$I.$$ There are 12 words starting with $$I.$$ This accounts up to the $$48^{th}$$ word. The $$49^{th}$$ word is $$NAAGI.$$
The $$50^{th}$$ word is $$NAAIG.$$