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

 = 24

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

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