Using the permutation table is quite easy. You initialize it with a length and a starting value, and it'll automatically randomize itself.
Problem is, you need to create a visual pseudo-shuffling animation. To that end you can still use a normal random call, but when it's time to pick a final number, you do so using the permutation table at the correct index.
Here's your modified example implementing what I explained :
https://drive.google.com/file/d/1HkqVTyFrRjg0AvcsHcTZXT25oTs_D_89/view?usp=sharing
Dude was really worth it. You showed me that I was making a mistake I was never going to guess, that index 1 of the permutation table is actually 0. How was I supposed to guess? So I was calling the index 1 from 1, when it's actually 0. And apart from that, I just changed your example by putting the table to generate not at the beginning of the layout, otherwise it would always be the same when clicking on the button, but I put it to generate when press the button and the variable is not starting.
Thanks for all the replies. Many told me that I would have to use matrix for this. Glad you won't need it. This forum is really good.