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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 :

JEE · Math · previous-year question

  1. A.$${{11!} \over {{{\left( {2!} \right)}^3}}}$$
  2. B.110
  3. C.56
  4. D.59correct

Answer

D. 59

Explanation

Here total no of different letters present are, (1) One M (2) Three E (E E E) (3) One D (4) One I (5) One T (6) Two R (R R) (7) Two A (A A) (8) Two N (N N) In the four letter word first letter is R and last letter is E. $$ \therefore $$ Word is = R _ _ E Now remaining letters are, M, EE, D, I, T, R, AA, NN Those 2 empty places can be filled with identical letters [EE, AA, NN] in 3 ways. Or two empty places can be filled with distinct letters [M, E, D, I, T, R, A, N] in $${}^8{C_2} \times 2!$$ ways. $$ \therefore $$ Total no of words = 3 + $${}^8{C_2} \times 2!$$ = 59

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