if all the letters of the word AGAIN bre arranged as in a dictonary, What is the 50th word?
There are total 5 letters in the word AGAIN in which A appears twice.
∴ The Required number of words
To get the number of words starting with A, we fix the letter A on the extreme left position then we rearrange the remaining three letters taken all at a time.
Hence the number of words starting with A = 4! = 4 × 3 × 2 × 1
Then, starting with G, the number of words
after placing G at extreme left position, we have letters A, A, I, N.
Similarly, there are 12 words which are starting with next letter I.
Thus, so far words obtained are 24 + 12 + 12 = 48
Now the 49th word starting with N in the dictionary will be NAAGI
∴ 50th word in dictionary order = NAAIG