Question

If all permutations of the letters of the word "AGAIN" are arranged as in dictionary, then fiftieth word is

• A. NAAGI
• B. NAGAI
• C. NAAIG
• D. NAIAG

Answer 1

Answer: (C)

NAAIG

Number of words starting with A are $4!=24$

Number of words starting with I are $\frac{4!}{2!}=12$

Number of words starting with G are $\frac{4!}{2!}=12$

Number of words till this$=24+12+12=48$, therefore two more words are required

NAAGI and NAAIG

$\therefore$fiftieth word is NAAIG