Shin Megami Tensei: Persona 4

Do skills get inherited random from parents (3-way fusion)?

I'm new to this game and I've been doing some experiments and it appears to me that in a 3-way fusion (as it ignores the order of the spread and looks at the highest level persona and fuse with the result of the 2 lower level parents) the skills it picks from the parents seem to be random. Does the order of the selection for the 3 way fusion affects the skills inheritance (lets ignore the skill restricted to be inheritance due to the fused persona type)?

I tried many times to shuffle the selection until I get the "good skills" I wanted from the parents to pass on to the fused one.

Note that I know there are certain skills that cannot be transffered to the fused persona. But I'm talking about which particular skills the fused persona accepts (if it can inherit from the parents). It seems this is random. Please confirm.

No, there doesn't seem to be any pattern to the way the skills are chosen when they can be transferred. At least, it didn't seem to be that case when I made my almost invincible Helel (nullifies or reflects everything, lol). It seems that all skills chosen can be from a mix of the three or even just one I think (I know it can be from just two of the three, since that's how I got the aforementioned Helel).

Maybe the one you are trying to fuse is a persona that really cannot transfer its skill there are some skills of persona's that cannot be transferable..