GAINESVILLE, Fla. -- His University of Florida players were spread across the family room at Billy Donovan’s home in Haile Plantation, eyes glued to the big-screen television on the wall, when their NCAA Tournament fate was revealed Sunday night.

The mood was subdued when CBS’ Greg Gumbel announced the Gators (23-10) had been tabbed as the No. 7 seed in the West Region and would face 10th-seeded Virginia (22-9) in Friday’s opening round (2:10 p.m., TNT) at Omaha, Neb.

A few seconds later, Donovan popped into the room.

“Congratulations, guys!” he yelled.

With that, UF officially had its third straight NCAA invite and the 12th in 16 seasons since Donovan arrived in 1996.

“We’re happy to be in the tournament,” freshman guard Bradley Beal said. “There are a lot of teams that don’t get this opportunity, so we’re fortunate to be in this situation.”

Even though Donovan didn’t necessarily agree with UF’s seeding -- “I thought we were closer to a 5 or a 6, but I don’t think it makes a lot of difference right now” -- the message to his team, which he took into his private home office for a pre-tournament heart-to-heart, was about getting there and the possibilities that come with it.

Remember how close the Gators were to the Final Four last year?

That was as a No. 2 seed. The path to giving themselves a similar chance this time will be far more difficult, but at least they’ve earned that chance.

“If you look at the teams with the best basketball traditions in the country -- North Carolina, Kansas, Kentucky, Duke -- you will see that those teams go to the NCAA Tournament more than anyone else,” Donovan said. “I’ve often said, ‘The tournament is like the lottery; you can’t win it, if you’re not in it.’ ”

You also can’t win it, without winning the first-round game, which was what Donovan and is staff went to work on mere minutes after the field of 68 teams was announced.

Though the season, UF video coordinator Oliver Winterbone recorded hundreds of nationally televised games. He immediately went back to the UF basketball complex to pull files of the Cavaliers from his library. More were expected to arrive later that night from various sources around the country, including the Atlantic Coast Conference Tournament, where UVa lost 64-61 n Friday’s semifinals against North Carolina State.

Assistant coach Norm Roberts, in his first year with the Gators, was head coach at St. Johns last year when his team had a preseason scrimmage against the Cavs, so he immediately was assigned the advance scout for the game.

“I know something about them,” Johnson said. “They’ll definitely want to slow it down.”

Virginia, coached by Tony Bennett, led the ACC in defense this season, holding opponents to a league-low 53.7 points per game and 39.6-percent shooting.

The Cavaliers have been rocked by injuries and transfers -- UVa dressed just seven players for one game late in the season -- but have the runner-up ACC Player of the Year in 6-foot-8, 237-pound forward Mike Scott, who averaged 18.1 points, 8.4 rebounds per game and led the conference in field-goal percentage at 56.2.

“I think Virginia is going to be interesting because you’re talking about contrasting styles of play,” Donovan said. “They’re a team that’s going to play maybe closer to the 50s against a team that’s trying to play into the 80s. Style of play will be very, very important.”

The winner of the Florida-Virginia game will face either second-seeded Missouri (30-4) or 15th-seeded Norfolk State (25-9) in second-round regional play next Sunday.

The Gators played their way down the bracket by losing four of their last five games, but they’ll certainly be battle-tested considering their last four opponents -- Kentucky twice, Vanderbilt and Alabama -- all made the NCAA field.

“And if Ohio State had won today [against Michigan State in the Big Ten title game], we would have had five games against No. 1 seeds,” Donovan said, citing three against Kentucky (No. 1 in the Southeast), one at Syracuse (No. 1 in East) and one at Ohio State (No. 2 in the East). “And most of those games were on the road.”

UF’s resume to the selection committee also included wins against the SEC and ACC tournament champions (Vandy and Florida State), though both of those victories were a while ago; the Commodores in January; Seminoles in December.

The team the Gators want to be in Nebraska -- if they want to get to the Sweet 16 in Phoenix the following weekend -- is the one that managed to set a fast tempo in a 74-71 loss to top-ranked UK Saturday and combined to make 21 3-point shots (including 11-for-22 against the Wildcats) at the SEC Tournament in New Orleans.

“We can play with any team in the country,” junior forward Erik Murphy said Sunday. “We just have to keep playing well, keeping playing together right now.”

They accomplished a key goal in just getting to this point. After all, you have to be in it to win it.

The Gators are in it. Again.

“The more opportunities you’re in it, the more opportunities you have to advance,” Donovan said. “And you know what? The more opportunities you’re in it, the more opportunities you have to get knocked out quickly. That’s gonna happen. That’s the nature of what you’re doing.”

And the fun.