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.

...