I'm sure this has been posted a bunch already, but oh well.

8 B1G teams:
It's possible for the B1G to get a team in 7 of the 8 Sweet 16 games.
If they all win up to the Sweet 16, 1 B1G team would eliminate 1 B1G team in the Sweet 16.
It's possible for 7 of the Elite 8 teams to be B1G teams.
The committee knocks the B1G from 8 down to 7 who can get past the Sweet 16.

7 Big 12 teams:
It's possible for the Big 12 to get a team in only 5 of the 8 Sweet 16 games.
If they all win up to the Sweet 16, 2 Big 12 teams would eliminate 2 Big 12 teams in the Sweet 16.
It's possible for 5 of the Elite 8 teams to be Big 12 teams.
The committee knocks the Big 12 from 7 down to 5 who can get past the Sweet 16.

And just FYI —

14 SEC teams:
It's possible for the SEC to get a team in each of the 8 Sweet 16 games.
It's possible for the SEC to get 2 teams in 3 of the 8 Sweet 16 games.
It's possible for all 8 of the Elite 8 teams to be SEC teams.