Out of 7 consonants and 4 vowels, words are to be formed by...

Three consonants out of 7 and 2 vowels out of 4 can be chosen in ${ }^7 \mathrm{C}_3 \times{ }^4 \mathrm{C}_2$ ways. Since each group contains 5 letters which can be arranged among themselves in 5 ! ways. Hence, the required number of words $$\begin{aligned} & =\left({ }^7 \mathrm{C}_3 \times{ }^4 \mathrm{C}_2\right) \times 5!=\frac{7!}{3!4!} \times \frac{4!}{2!\times 2!} \times 5! \\ & =\frac{7 \times 6 \times 5 \times 4!}{3 \times 2 \times 4!} \times \frac{4 \times 3 \times 2!}{2 \times 1 \times 2!} \times 5 \times 4 \times 3 \times 2 \times 1 \\ & =35 \times 6 \times 120=35 \times 720=25200 . \end{aligned}$$