From 5 consonants and 5 vowels, how many words can be formed using 3 consonants and 2 vowels?

We have to form words using $3$ consonants and $2$ vowels from $5$ consonants and $5$ vowels.

So, firstly we will select consonants and vowels.

This can be done in ${}^{5}C_3\times {}^{5}C_2$ ways.

Now, these $5$ letters needs to be arranged

So, total number of words formed are ${}^{5}C_3\times {}^{5}C_2\times 5!$

$=\frac{5\times 4}{2}\times \frac{5\times 4}{2}\times 5\times 4\times 3\times 2$

$=12000$.