The No. 11-seeded Friars won the Big East Tournament championship on Saturday.
Awaiting the winner of UNC-Providence will be Iowa State or NC Central.
"The NCAA Tournament is always an exciting time and I am so pleased for our kids," Williams said. "They have overcome a lot and put themselves in a position to play in the Tournament. We have had some outstanding wins this year, both in and out of league play, over teams that received some very high seeds in the field, so we know we are capable. But we must play better than we have over the last two weeks if we want to reach our big-time dreams.
"I am glad we play on Friday as that gives us an extra day to practice and prepare for our game against Providence."
This is the third time UNC has been a No. 6 seed (1996, 2004).
Roy Williams has a 28-7 record in the NCAA Tournament at UNC.