Find the number of words formed (meaningful or meaningless) by the letters of the words `AGAIN` .If we write these words in a dictionary, find it `50^(th)` word.

Answer

50

Explanation

These are 5 letters in the word 'AGAIN' in which A occur twice.
Total words `(5!)/(2!) = (120)/(2) = 60`.
In a dictionary, all words are arranged in the order of English alphabets.
Words starting with A:
Keeping the position of A fixed, no of words forming by the remaining letters `A,G,I,N = 4! = 24`.
Again, keeping the position of G fixed, no of words forming by the remaining letters
`A,A,I,N = (4!)/(2!) = (24)/(2) = 12`
Again, keeping the position of I fixed, no of words forming by the remaining letters
`A,A,G,N = (4!)/(2!) = (24)/(2) = 12`
Total words formed upto this stage `= 24 +12 +!2 = 48`
49th word = NAAGI
50th word = NAAIG.