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.

  • $\begingroup$ 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? $\endgroup$ – Ian Coley Apr 17 '13 at 19:34

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.

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