Question

The number of four-letter words that can be formed (the words need not be meaningful) using the letters of the word 'MEDITERRANEAN’ such that the first letter is $E$ and the last letter is $R$, is

• A. $\frac{11!}{2!·2!·2!}$
• B. $59$
• C. $56$
• D. $\frac{11!}{3!·2!·2!}$
• E. $\frac{11!}{3!·3!·2!}$

Answer 1

The correct option is B

$59$

Explanation for the correct option:

Find the required number of a four-letter words.

The word 'MEDITERRANEAN’ is given.

Find the number of four-letter words that can be formed from the given word such that the first letter is $E$ and the last letter is $R$ as follows:

In the given word there are $13$ letters in total.

Since the two letters, $E$ and $R$ have a fixed place. So, we don't have to select and arrange these letters.

So, now we only have to select two letters only.

So, We have $11$ letters left out of which $2E\text{'}s$, $2N\text{'}s$, $2A\text{'}s$.

So, the total number of ways to select the two different letters are $8·7=56$.

The total number of ways to select the two same letters are $3$.

So, the total number of required four-letter words is $56+3=59$.

Therefore, the total number of four-letter words that can be formed from the given word such that the first letter is $E$ and the last letter is $R$ is $59$.

Hence, option $B$ is the correct answer.