Find all permutations of number from 1 to 6 where 5 always before 1

I'm trying to help my son with his homework and I'm out of my depth :(

As the question states, it look to me that I can concentrate on 5 and 1. so it will look li this:

[5,1,X,X,X,X] => 4!
[5,X,1,X,X,X] => 4!
[5,X,X,1,X,X] => 4!
[5,X,X,X,1,X] => 4!
[5,X,X,X,X,1] => 4!

[X,5,1,X,X,X] => 4!
[X,5,X,1,X,X] => 4!
[X,5,X,X,1,X] => 4!
[X,5,X,X,X,1] => 4!

[X,X,5,1,X,X] => 4!
[X,X,5,X,1,X] => 4!
[X,X,5,X,X,1] => 4!

[X,X,X,5,1,X] => 4!
[X,X,X,5,X,1] => 4!

[X,X,X,X,5,1] => 4!

so we end up with 4! * 15

Is this correct?

This is just me counting on my fingers ;), What would be the "Combinatorial" way of thinking and solving this kind of questions?

Thank you.

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