Question

If all the permutations of the letters in the word $OBJECT$ are arranged in alphabetical order as in a dictionary. The $717th$ word is

• A. $TJOECB$
• B. $TOJECB$
• C. $TOJCBE$
• D. $noneofthese$

Answer 1

The correct option is C $TOJCBE$

The words are arranged in alphabetical order then the first $5!=120$ words will start with the letter B. The next set of 120 words each will start with letters C, E, J and O respectively.
Therefore there will be 600 such words.
Now the 601st word will start with letter T and there will be 4! word where the 2nd letter is B.
Similarly The next set of 24 words each will have the second letter C, E, and J respectively.
Therefore there will be 600 + 96 = 696 words in alphabetical order.
So the next word will have the letters TO.
Continuing in similar format, there are 6 words each with the third letter as B, C, and E.
Hence the total word are 696 +18 = 714.
The 715th word will be TOJBCE;
716th word will be TOJBEC;
and 717th word will be TOJCBE.