Explanation

(c)
Given word is EAMCET
Here number of vowels are 3 $ie$, E, A, E and number of consonants are 3, $ie$, M, C, T and number of ways of arranging three consonants$= 3! = 6$
V C V C V C V
In the places ‘V’, we shall arrange vowels
There are 4 places marked V
$\therefore$ Number of ways of arranging vowels
$= {\ ^{4}P}_{3} + \frac{1}{2} = 12$ [$\because$ E is repeated twice]
$\therefore$ Total number of words$= 6 \times 12 = 72$