If the four letter words (need not be meaningful) are to be formed using the letters from …

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:

Accepted Answer

Here total no of different letters present are,

(1)   One M

(2)   Three E (E E E)

(3)   One D

(4)   One I

(5)   One T

(6)   Two R (R R)

(7)   Two A (A A)

(8)    Two N (N N)

In the four letter word first letter is R and last letter is E.

$$ \therefore $$     Word is = R \_ \_ E

Now remaining letters are,

M, EE, D, I, T, R, AA, NN

Those 2 empty places can be filled with identical letters [EE, AA, NN] in 3 ways.

Or two empty places can be filled with distinct letters [M, E,  D, I, T, R, A, N] in $${}^8{C_2} \times 2!$$ ways.

$$ \therefore $$   Total no of words = 3 + $${}^8{C_2} \times 2!$$ = 59

Solutions · 1