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 :
My attempt:
$4$ different letters, $3E, 2R, 2A, 2N$. i.e. total $8$ varieties, out of $13$ letters.
Since the first and the fourth letter is fixed, so the intermediate two letters are to be filled from $11$ remaining letters. But we can't just do $^{11}C_2$ as all $11$ are not different. Also, $^8C_2$ won't make sense either as that won't include the option of $2N$ or $2A$ etc.
How to go about it?
Best Answer
The two middle places are to be filled from
$$ \{ M,D,T,I,R \} \quad \{ 2\cdot E,2\cdot A,2\cdot N \}$$
We have following two cases :
or as pointed by @Intelligenti pauca, simply $8 \cdot 7 = 56$
Total $= 59$