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 :
- $\frac{11!}{(2!)^3}$
- $110$
- $56$
- $59$
The Correct Option is D
Solution and Explanation
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
\(3+^{8}P_{2}=59\)
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