Rank of the word THING in the dictionary of words formed by letters of the word THING.


could anybody please explain it clearly.

• On arranging the letters in order we get
  G, H, I, N, T
  T is 5th letter
  then G, H, I, N
  H is 2nd letter
  then G, I, N
  I is 2nd letter
  then G, N
  N is 2nd letter
  then G
  total no. of words = 5*4*3*2*1 = 120
  so rank = (120/5)*4+(24/4)*1+(6/3)*1+(2/2)*1+1
  = 96+6+2+1+1 = 106
• 11 years agoHelpfull: Yes(3) No(1)
• on arranging the letters in order we get G H I N T
  now consider the word 'THING'
  we have first letter 'T' now see in arranging order we have 4 letters(G H I N)bfor 'T' now remove cut the 'T'
  so 4*4!
  after 'T' we have 'H' in arranging order we have 1 letter(G) before 'H' so 1*3!now cut 'H' like this for 'I' 1*2!
  for N 1*1!
  so rank=4*4! + 1*3! + 1*2! + 1*1! + 1(for last letter 'G') =106
  NOTE-this short trick is only for nonrepititive words.
• 11 years agoHelpfull: Yes(1) No(0)
• 106
  
  The no. of words formed = 5! = 120
  
  Alphabetically, total no. of words formed with G,H,I,N = 4*(1*4!) = 96
  
  Taking first letter as T and second letter as G 6 words are formed.
  
  Next, first letter as T and second letter as H:
  
  THGIN
  THGNI
  THIGN
  THING 1+1+1+1 = 4
  
  Rank = 96 + 6 + 4 = 106
  
• 11 years agoHelpfull: Yes(0) No(1)