Number of ways of selecting 3 consonants out of 7 = ⁷C₃
Number of ways of selecting 2 vowels out of 4 = ⁴C₂
Number of ways of selecting 3 consonants out of 7 and 2 vowels out of 4 = ⁷C₃ x ⁴C₂

$$\begin{gathered} =\left(\frac{7\times 6\times 5}{3\times 2\times 1}\right)\times \left(\frac{4\times 3}{2\times 1}\right) \\ =210 \end{gathered}$$

It means that we can have 210 groups where each group contains total 5 letters(3 consonants
and 2 vowels).
Number of ways of arranging 5 letters among themselves = 5!
= 5 x 4 x 3 x 2 x 1 = 120
Hence, Required number of ways = 210 x 120 = 25200