If the four letter words (need not be meaningful) are to be formed using the letters from the word &quot…

If the four letter words (need not be meaningful) are to be formed using the letters from the word "MEDITERRANEAN" such that the first letter is R and the fourth letter is E, then the total number of all such words is :
  1. 110
  2. 59
  3. 11!2!3
  4. 56

Solution

M,EEE,D,I,T,RR,AA,NN

R_ _ _ E_

Two empty places can filled with identical letters EE, AA, NN ⇒ 3 ways

Two empty places, can be filled with distinct letters M,E,D,I,T,R,A,N ⇒   8P2

∴ Number of words 3+8P2=59

Asked in: JEE Main 2016 (09 Apr Online)

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