Question

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 :

• A. $\frac{11!}{(2!)^3}$
• B. $110$
• C. $56$
• D. $59$

Answer 1

The Correct Option is D

M, EEE, D. I, T, RR, AA, NN 
\(\frac{R}{ }--\frac{E}{ }\) 
Two empty places can be filled with identical letters [EE, AA, NN] \(\Rightarrow\) 3 ways 
Two empty places, can be filled with distinct letters [M, E, D, I, T, R, A, N] \(\Rightarrow ^{8}P_{2}\)
\(\therefore\) Number of words 3+56=59

or

 \(3+^{8}P_{2}=59\)