# How many seven letter sequences with no repeated letters contain all five vowels

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.

• The five vowels are given, so pick two different consonants. How many choices are there? Now you can shuffle the letters in any order. How many choices for that? Apr 17 '13 at 19:34