How many different four letter words can be formed (the words need not be meaningful) using the letters of the word "MEDITERRANEAN" such that the first letter is E and the last letter is R?

A. 59

B. 11!/2!*2!*2!

C. 56

D. 23

E. 11!/2!*2!*2!*3!

• The first letter is E and the last one is R.
  
  Therefore, one has to find two more letters from the remaining 11 letters.
  
  Of the 11 letters, there are 2 Ns, 2Es and 2As and one each of the remaining 5 letters.
  
  The second and third positions can either have two different letters or have both the letters to be the same.
  
  Case 1: When the two letters are different. One has to choose two different letters from the 8 available different choices. This can be done in 8 * 7 = 56 ways.
  
  Case 2: When the two letters are same. There are 3 options - the three can be either Ns or Es or As. Therefore, 3 ways.
  
  Total number of possibilities = 56 + 3 = 59
  
• 11 years agoHelpfull: Yes(14) No(6)
• solution:A)59
  MEDITERRANEAN (13 LETTERS) - ER( 2 letters)= 11 letters
  case1)considering blank spaces to be filled by repeated letters( NN,AA,EE)there will be 3 ways.(11-3=8 remaining letters)
  case2) considering non repeated letters can be arranged in 8P2 ways.
  hence total arrangements= 8p2+3= 56+3=59
  
• 11 years agoHelpfull: Yes(9) No(0)
• option E is the correct answer.because total number of words in MEDITERRANEAN are 13,now E and R are fixed at first and last position...remaining words are 11.which can be arranged in 11! ways..
  11!/2!*2!*2!*3!
• 11 years agoHelpfull: Yes(4) No(15)
• 59 ways.
  e_ _r
  3 ways(aa,nn,ee) remaining letter=8
  8c1*7c1=56
  56+3=59
• 9 years agoHelpfull: Yes(3) No(0)
• for all those with ans 59 guys if u carefully observe there are 3 E ,2R, 2N, 2A in the letter MEDITERRANEAN so all possible ways such that start with E and end with R =
  11!/2!2!2!3!
• 7 years agoHelpfull: Yes(1) No(0)
• Given that E and R is fixed at first & last position, therefore remaining 11!/(3!*2!*2!*2!). Repetiton:3!-E, 2!-R,2!-A,2!-N.
• 11 years agoHelpfull: Yes(0) No(1)