The letters in the word ADOPTS are permuted in all possible ways and arranged in alphabetical order then find the word at position 42 in the permuted alphabetical order?	Choose the correct choice from the following.
A) AOTDSP  B) AOTPDS  C) AOTDPS  D) AOSTPD  E) None of these
Explanation :   In alphabetical order : A D O P S T   A _ _ _ _ _ : the places filled in 5! ways = 120, But we need a rank less than 120. So the word starts with A.   A D _ _ _ _ : empty places can be filled in 4!=24   A O _ _ _ _ : the places filled with 4! ways = 24. If we add 24 + 24   this total crosses 42. So We should not consider all the words starting with AO.   A O D _ _ _ : 3!= 6   A O P _ _ _ : 3!=6   Till this 36 words are obtained, we need the 42nd word.   AOS _ _ _ : 3!= 6   Exactly we are getting the sum 42. So last 3 letters in the descending order are TPD.   So given word is AOSTPAOSTPD   Answer : AOSTPD
<result>D</result>
The letters in the word ADOPTS are permuted in all possible ways and arranged in alphabetical order then find the word at position 42 in the permuted alphabetical order?