[Math] How many seven letter sequences with no repeated letters contain all five vowels

Question

I can't seem to get the right answer with this.

How many seven letter sequences of English letters, with no repeated letters, contain all five vowels?

So far I am doing $\dbinom{21}{2} \cdot 5^5 \cdot 2^2$. This is still not right. Please help, I need to understand how to do this.

Answer 1

Hint: you need all five vowels and two consonants. How many ways are there to pick the two consonants? How many ways to pick which two slots hold consonants? How many ways to order the vowels? How many ways to order the consonants? Now multiply.