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Previous Year Question (PYQs)
2
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, then the $50$th word will be
Solution
Letters: A, A, G, I, N
Words starting with A:
$ \frac{4!}{2!}=12 $
Starting with G:
$ \frac{4!}{2!}=12 $
Starting with I:
$ \frac{4!}{2!}=12 $
Total till I: $12+12+12=36$
Next start with N
Remaining: A, A, G, I
Arrangements:
$ \frac{4!}{2!}=12 $
So positions $37$ to $48$
$49^{th}$ word = NAAGI
$50^{th}$ word = NAAIG
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