Eleven times.
UCLA has appeared in 18 Final Fours: 1962, 1964, 1965, 1967-1976, 1980, 1995, 2006-2008. The 1980 Final Four was vacated by the NCAA due to violations, but technically, UCLA has appeared in 18 Final...
West Virginia has been to the Final Four 2 times: 1959 and 2010.
2010 is Butler's first time in the final four so 1.
I can answer that one for you a big 0 Rockchalk Jayhawk