Question

If the four letter words (need not to meaningful) are to be formed using the letter 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. $110$
• B. $59$
• C. $\frac{11!}{(2!{)}^3}$
• D. $56$

Answer 1

Answer: (B)

$59$

First letter is $R$ and Fourth letter is $E$.

So now we have $11$ letters left with $2E,2A,1M,1D,1I,1T,1R$ and $2N$ And with this we have to form a two-letter word.

There will be $2$ cases when both these two letters of the middle will be the same. And this will be when they both are either $EE,AA$ or $NN$.

Now when middle two letters are not same. So we have to form a $2letter$ word with $8letters$ without repetition .

Number of such words will be $8\times 7=56$

Hence, the total number of such four-letter words with $R$ as the first letter and $E$ as the last letter will be $56+3=59$.