6
They havent won any national championships
University of North Carolina at Chapel Hill
For the major sports, Alabama for football, UCLA for basketball, and LSU and South Carolina for baseball
40 national championships, 38 ncaa national championships
University of Kentucky
none
UCLA Bruins
The University of North Carolina does not have any national championships in football.
Zero
Duke men's basketball has won 4 national championships: 1991, 1992, 2001, and 2010.
ZERO
The Kentucky men's basketball team has won seven national championships, won in 1948, 1949, 1951, 1958, 1978, 1996 and 1998.