"Permutations" train

Array programming
1

We discussed permutations in our math tutoring today. P(10,4) in APL is (!10)÷!6.

But how to do this as a train / tacit function? It’s not 10(!÷!)6, because the outside functions apply dyadically. I’m guessing there’s some composition approach to this, but I haven’t figured it out yet…

2

⍥ does this sort of ‘preprocessing’ of both arguments, so ÷⍥!
a (f⍥g) b is (g a) f (g b)

EDIT: I missed the subtraction, so it’s ⊣÷⍥!-

3

Perfect - thank you!

4

Here’s the tree view of the expression from @rak1507 :

┌─┼─┐
⊣ ⍥ -
 ┌┴┐
 ÷ !

It’s a fork!