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

Answer: (D)

$59$

Answer 2

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

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