I am not sure how to answer your question but I will tell you how I work it out .
My beds are heavy on perennials so my annuals come up between them . If I want a specific color or flower I lay down a square (rubber flexible stepping not/ stone) to save a space in the fall when i do clean-up. then in the spring I ether spread seed or in most cases I plunk plants into the spaces.
I have a small green house where I start most plants. I am bad at keeping weeds out so they will some times take over before the seedlings get a good start.
as for random
I know odd numbers always look more random
I often do three in a triangle then a loner off just a bit
I tend a large garden in town and the owner goes with 5 or 7 , groupings look best in a big garden because color gets lost in most single plants unless it is a bush.
Good luck
I always remember a garden is a living constant changing thing so every season you have another chance to get what you are looking for.
