Join the Most Relevant JEE Main 2025 Test Series & get 99+ percentile! Join Now
Search any question & find its solution
Question: Answered & Verified by Expert
If all the seven letters of the word LEADING are permuted in all possible ways and the words thus formed are arranged as in the dictionary order, then the word in 2017th place is
MathematicsPermutation CombinationAP EAMCETAP EAMCET 2018 (25 Apr Shift 1)
Options:
  • A ELIGDAN
  • B ELNADGI
  • C ELINADG
  • D ELNDAGI
Solution:
2321 Upvotes Verified Answer
The correct answer is: ELNADGI

First we will arrange the letters of the word LEADING in the alphabetical order.

A,  D,  E,  G,  I,  L,  N

Number of words staring with letter A=6!=720

Number of words staring with letter D=6!=720

Number of words staring with letter E=6!=720

Total words are 720+720+720=2160>2017.

Hence, the required word will start from the letter E and before E we have total 720+720=1440 words.

Now,

Number of words staring with letters EA=5!=120

Number of words staring with letters ED=5!=120

Number of words staring with letters EG=5!=120

Number of words staring with letters EI=5!=120

Total words=1440+120+120+120+120=1920

Number of words staring with letters EL=5!=120

Total words

=1920+120=2040>2017

Hence, the required word will start from letters EL. And, words before EL are 1920.

Now,

Number of words staring with letters ELA=4!=24

Number of words staring with letters ELD=4!=24

Number of words staring with letters ELG=4!=24

Total words

=1920+24+24+24=1992

Now, 

Number of words staring with letters ELI=4!=24

Now, total words=1992+24=2016

Number of words staring with letters ELN=4!=24

Total words =2016+24>2017

Hence, required word is ELNADGI

Looking for more such questions to practice?

Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.