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  4. 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 :

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Q. 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 MainJEE Main 2016Permutations and Combinations

Solution:

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 $3+^{8}P_{2}=59$