If the letters of the word CHASM are rearranged to form 5 letter words such that none of the word repeat and the results arranged in ascending order as in a dictionary what is the rank of the word CHASM?

• let us rank the letters a-1,c-2,h-3,m-4,s-5
  so we hae to acheie the arrangement 23154
  there are 24 numbers starting with 1
  so 25th letter will be 21345
  there will be 6 letter which start with 21
  so 30th letter will be 21543
  31th will be 23145
  and 32nd will be 23154 which is req number
• 12 years agoHelpfull: Yes(12) No(2)
• Admin Please explain 120*(2-1)/5 + 24*(2-1)/4 + 6*(1-1)/3 + 2*(2-1)/2 + 1
  
  (2-1)/5 ?
  (1-1)/3 ?
• 12 years agoHelpfull: Yes(8) No(1)
• 32th word is correct
• 13 years agoHelpfull: Yes(7) No(1)
• The 5 letter word can be rearranged in 5!=120 Ways without any of the letters repeating.
  
  The first 24 of these words will start with A.
  
  Then the 25th word will start will CA _ _ _.
  The remaining 3 letters can be rearranged in 3!=6 Ways. i.e. 6 words exist that start with CA.
  
  The next word starts with CH and then A, i.e., CHA _ _.
  The first of the words will be CHAMS. The next word will be CHASM.
  
  Therefore, the rank of CHASM will be 24+6+2= 32
  
  
  
• 9 years agoHelpfull: Yes(4) No(1)
• there will be 5! words = 120 words
  and the word CHASM will be 31st word when arranged in dictionary order.
• 13 years agoHelpfull: Yes(3) No(9)
• first, fix A then there will be 24 words starting with A. then 25th word will start with C.Now fix C and A there will be 6 more words. (till now total 30). 31st word will be CHAMS and then 32nd will be CHASM.
• 10 years agoHelpfull: Yes(3) No(0)
• The letters when arranged alphabetically are : ACHMS
  now we have to find rank of CHASM so
  words starting with C are given by C _ _ _ _ i.e 4! =24
  now next we have to take CH _ _ _ i.e, 3!= 6
  next alphabet according to our alphabets is 'A' given by words starting with CHA _ _
  here we have two possible arrangements either CHAMS which will be the 31st word
  secondly CHAMS will be having a rank of 32nd.
  
  Hence our answer is 32.
• 7 years agoHelpfull: Yes(2) No(0)
• please explain all the solution clearly.
• 7 years agoHelpfull: Yes(1) No(0)
• Consider a coding system where C, H, A, S, M = 2, 3, 1, 5, 4 respectively. We want to know the rank of code 23154.
  
  Let's count all of the possible combinations below 23154.
  
  We know that any code starting with 1 is less so we have 4! = 24 possibilities.
  
  We also know that any cod starting with 21 is less so we have 3! or 6 additional possibilities.
  
  For codes starting with 23XXX, only 23145 is less than 23154. so we have a total of 31 codes less than 23154 so the rank of cod 23154 is 32 and the answer, IMO, is (3).
  _________________
  Best,
  
• 9 years agoHelpfull: Yes(0) No(0)