Find the number of words with or without meaning which can be made using all the letters of the word AGAIN. If these words are written as in a dictionary, what will be the 50th word?

Explanation

(i) The given word 'AGAIN' consists of 5 letters, out of which there are 2 A's and the rest are all distinct.
Hence, the number of words formed by using all the letters of the given word `=(5!)/(2!)=60.`
(ii) When the letters of the word 'AGAIN' are listed in a dictionary, the first word would be AAGIN.
Starting with A and arranging the remaining 4 letters A, G, I, N, we oibtain 4 ! words, i.e., 24 words.
The 25th word would be GAAIN, which starts with G.
Now, starting wilth G arrange the remaining 4 letters AAIN, (in which A occurs 2 times and the rest are different) in all possible ways.
Number of such arrangements `=(4!)/(2!)=12.`
Thus, we obtain 12 new words.
The 37th word would be IAAGN, which starts with I.
Now, starting with I and arranging the remaining 4 letters,
AAGN, we get `(4!)/(2!)=12` words.
The 49th word would be NAAGI and hence the 50th word is NAAIG.