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 :

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) (11!/(2!)3) (B) 110 (C) 56 (D) 59

Tardigrade Admin · Accepted Answer

M, EEE, D. I, T, RR, AA, NN (R/ )--(E/ ) Two empty places can be filled with identical letters [EE, AA, NN] ⇒ 3 ways Two empty places, can be filled with distinct letters [M, E, D, I, T, R, A, N] ⇒ 8P2 ∴ Number of words 3+8P2=59

Q. If the four letter words (need not be meaningful ) are to be formed using the letters from the word $" ME D I TERR A NE A N "$ such that the first letter is $R$ and the fourth letter is $E$ , then the total number of all such words is :

$\frac{11 !}{( 2 ! ) ^{3}}$

$110$

$56$

$59$

M, EEE, D. I, T, RR, AA, NN
$R - - E$
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] $\Rightarrow^{8} P_{2}$
$∴$ Number of words $3 +^{8} P_{2} = 59$

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 :

(2!)311!​

110

56

59