Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2 vowels can be formed?

Answer: Option C

Number of ways of selecting (3 consonants out of 7) and (2 vowels out of 4)
$$\begin{array}{rl}& =\left({}^7{C}_3\times {}^4{C}_2\right)\\ & =\left(\frac{7\times 6\times 5}{3\times 2\times 1}\times \frac{4\times 3}{2\times 1}\right)\\ & =210\end{array}$$
Number of groups, each having 3 consonants and 2 vowels = 210
Each group contains 5 letters.
Number of ways of arranging 5 letters among themselves
= 5!
= 5 x 4 x 3 x 2 x 1
= 120
∴ Required number of ways = (210 x 120) = 25200