Out of $7$ consonants, the number of ways of selecting $3$ consonants $={ }^{7} C_{3}$
Similarly, number of ways of selecting
$2$ vowels out of $4$ vowels $={ }^{4} C_{2}$
$\therefore $ Total number of words formed
$={ }^{7} C_{3} \times{ }^{4} C_{2} \times{ }^{5} P_{5}$
$=\frac{7 \times 6 \times 5}{3 \times 2 \times 1} \times \frac{4 \times 3}{2 \times 1} \times 5 !$
$=7 \times 5 \times 2 \times 3 \times 120=25200$