My understanding is that #8nmc can be attached to the bottom of joists, but
#10nmc must run through holes in them. Is that correct?

I need to run two new cables, a 10/3 and a 12/2. If I ran them together,
they would have more mass than a 8/2. Can I attach them to the bottom of
the joists, or is code real specific on the matter?

Thanks.