Class 11

Math

Algebra

Permutations and Combinations

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:

- $110$
- $59$
- $(2!)_{3}11! $
- $56$

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 $3$ 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 $8×7=56$

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