All letters of the word ‘AGAIN’  are permuted in all possible ways and the words so formed (with or without meaning) are written as in dictionary, then fiftieth word writtenas in dictionary, then the fiftieth word is

First, we arrange the words which begin with A. There are 4 other letters, all distinct to fallow AS to from different words. They can be arranged in $\overline{)4}=24$ ways. Hence, there are 24 words which begin with A. the words beginning with A will be followed by those, which begin with G. When G fixed in the first place there are four letters (of which h two are A’s) to be arranged and this can be done in $\frac{\overline{)4}}{\overline{)2}}=12$  ways. So 24 words begin  with A, 12 with G and hence 37 th word begin

With I and there are $\frac{\overline{)4}}{\overline{)2}}=12$  words which being

With I since there are 4 letters (of which two A’s) to follow I. When the words beginning with I have been written, there will be 48 words in the list. The 49^th word begin with N and is NAAGI and the 50 th words is NAAIG