Question

The English alphabet has $5$ vowels and $21$ consonants. How many words with two different vowels and $2$ different consonants can be formed from the alphabet?

Answer 1

We need $2$ vowels and $2$ consonants. So first we need to choose them and then they can be arranged.

Choosing = $5C_2{\times }^{21}{C}_2$

They can be arranged in $4!$ ways.

So total number of words are $4!\times 5C_2{\times }^{21}{C}_2$