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 arranged in a dictionary, what will be the 50th word?
The word AGAIN has 5 letters in which A is repeated 2 times.
Therefore, the required number of possible words
While arranging these words in the dictionary, the words beginning with A will come first.
For this, fixing the first letter as A, we arrange the remaining 4 letters taken all at a time. Note that all the remaining 4 letters are different.
So, the number of words starting with A is 4! = 24.
Next fixing G in the first position, we have 4 remaining letters in which 2 are of one kind.
Then, starting with G, the number of words
Similarly, fixing letter I in the first place, the number of words so obtained are 12.
Total number of words so far obtained = 24 + 12 + 12 = 48.
The next word would definitely begin with letter N.
The 49th word is NAAGI and the 50th word is NAAIG.
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