I'm new to combinatorics, Although I understood most of the concepts this one baffles me.
How many words exist that have exactly $5$ distinct consonants and $2$ identical vowels?
The Answer is $$\binom{21}{5} \binom{5}{1} \frac{7!}{2!}$$
My doubt is: Why do we write $\binom{5}{1}$ when we have to select 2 vowels?(Answers with examples appreciated).
Since we have 2 identical vowels, we should to choose only one "kind" of vowels to put it in two places.