Question

If all permutations of the letters of the word 'AGAIN' are arranged as in dictionary, then fiftieth word is equal to:

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

Answer 1

The correct option is C

NAAIG

Explanation for the correct option:

Find the fiftieth word of 'AGAIN' in particular order:

Total number of words in 'AGAIN' are $5$

In 'AGAIN' $A$ is repeated twice.

Now,

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

Number of words starting with $I$ are $2!4!=12$

Number of words starting with $G$ are $2!4!=12$

Total number of words till now $=24+12+12$

$=48$

$\Rightarrow$Two more words are still remaining which are NAAGI and NAAIG

$\therefore$Fiftieth word is NAAIG

Hence, Option ‘C’ is Correct.