The letter in the word ADOPTS are permuted in all possible ways and arranged in the alphabetical order. Find the word at position 42 in the permuted alphabetical order.

• Answer- AOSTPD
  
  No. of words starting with AD=4!=24, AO=4!
  Thus the word has to start with AO because the last word with AO will be the 48th word.
  Now no. of words formed with AOD=3!=6, AOP=3!=6, AOS=3!=6 Thus the last word formed with AOS is=4!+3!+3!+3!=24+6+6+6=42
  Thus the last word formed with AOS is AOSTPD
• 11 years agoHelpfull: Yes(71) No(15)
• AOSDPT is the answer
  
• 11 years agoHelpfull: Yes(16) No(17)
• No of words starting with AD=24;
  No of words starting with AO=24;
  but we want 42nd letter ,so'll start counting words starting from AOD=6;
  AOP=6;
  AOS=6;
  the last word of AOS_ _ _ is 42nd letter and that is AOSTPD
• 11 years agoHelpfull: Yes(13) No(3)
• AD---- 4!=24 words
  AO---- 4!=24 words....exceeds 42nd term
  so,
  ADO--- 3!=6 words
  ADP--- 3!=6 words
  ADS--- 3!=6 words
  the last word of this combination will be 42nd word.
  therfore the ans is ADSOPT
• 11 years agoHelpfull: Yes(10) No(12)
• please explain how is TPD after AOS????? i think it should be DPT...
• 11 years agoHelpfull: Yes(9) No(4)
• plz koi thk se samjha do.................
• 11 years agoHelpfull: Yes(9) No(4)
• AOSDPT.....is the correct solution of this problem
  
• 11 years agoHelpfull: Yes(6) No(5)
• ADSOPT is the answer
• 11 years agoHelpfull: Yes(4) No(9)
• 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 AOSTPD
  
• 9 years agoHelpfull: Yes(4) No(2)
• 1. ADOPST
  .
  .
  23. ADTSPO
  24. AODPST
  .
  .
  29. AOTSPD
  30. AOPDST
  .
  .
  35. AOPTSD
  36. AOSDPT
  .
  .
  41. AOSTPD
  42. AOTDPS
  ANS is AOTDPS
• 11 years agoHelpfull: Yes(3) No(11)
• mr. ray 7 mr. paul, u r finding the 47th word as AOSTPD
  but it is asked the 42nd word so it is simply AOSDPT
• 11 years agoHelpfull: Yes(2) No(0)
• It's AOSTPD Ans.
• 11 years agoHelpfull: Yes(0) No(0)