permutations of letters in VERTICAL beginning w/ 3 vowels

[AmySaunders]

I am working through Saxon Advanced Mathematics and need help understanding this question:

How many permutations of the letters in the word vertical begin with three vowels?

[stapel_eliz]

You only have the three vowels, which limits your options nicely.

You'll have E, I, and A at the beginning. In how many ways can these three be permuted?

You'll have V, R, T, C, and L at the end. In how many ways can these five be permuted?

Once you have the numbers of options of each independent outcome, apply the Basic Counting Principle by multiplying these numbers to get the required total number of options.

[AmySaunders]

So it's 3! x 5! = 720. Thank you SO much. I understand!