What was billed as "the only means" of giving 4,700 people an "equal opportunity" to purchase 179 condominium units in a major Alexandria apartment complex turned into an angry uproar yesterday amid charges of cheating and chicanery.

The cries erupted midway through a lottery designed to award chances to purchase the moderately-priced Parkfairfax units, located off Shirley Highway, about five minutes from downtown Washington. The 1,684-unit project, which once served as the Washington home for Richard Nixon and Gerald Ford when they were in Congress, is being converted to condominums and developer Giuseppe Cecchi said the project had attracted far more bidders than his staff could handle.

But yesterday morning as Cecchi stuck his gold cufflinked wrist into a wire drum, pulled another of the green coupons out and announced the 100th winner, the crowd of 300 would-be home-owners under a red and white tent turned ugly.

A woman squealed - but it wasn't the winner. "That's the third time that name has been called," shouted Gloria Popps, seated on a folding chair near the Parkfairfax officials. "It's not fair."

The crowd of men, women and children - who had been fortfied on free cups of Pepsi and patience - echoed with shouts of "rip-off."

"It's a cheat," said Mike Horrocks, a 35-year-old school teacher from Gaithersburg. "I'm burned up about the whole thing. Anybody could have run a lottery better than this.They had four tables of four different locations to register. What's to prevent somebody from putting his name in more than once?"

Nothing, answered Cecchi, as tiny bead of sweat trickled down his face toward his white french-cut shirt.

"We said in the instructions that each person fill out one ticket," said Cecchi. "It's apparent that some people did not abide by the rules. We're trying to be fair. We couldn't use CIA tactics, asking people for their IDs. I'm not God. I'm not here to punish people."

The reason for the lottery, Secchi pointed out, was to prevent what happened the last time condominiums went on sale at the Parkfairfax. More than 50 people camped in the rain one night last fall before the first group of apartments went on sale.

The first-come first-served method was abandoned by International Developers Inc. of Washington, in favor of yesterday's randam drawing. But several peole said they would have preferred a line to what happened yesterday.

"I heard one man's name called three times," Dean Popps, a 30-year old law student, said. "I think they should be disqualified."

Cecchi, president of International Developers, stopped his salesmen from completing any of the sales after all of the coupons were drawn. He then consulted his lawyers and issued a statement.

"The lawyers said we should abide by the rules in estabilshing the priority list." For people who put in more than one ticket Cecchi said his firm would honor only one ticket. "I think that's as fair as we can be."

As for the next lottery, Cecchi said, "We'll just tell them, 'Don't do that.' Maybe we'll say it a little more forcibly."

Among yesterday's bidders on the one and two-bedroom garden apartments which start at $27,000, was Alexandria socialite and scarf designer Frankie Weich. When her name was called, an unidentified man picked up the ticket, made an appointment to sign a purchaser's agreement and signed the yellow legal pad "Frank Welch."

After it was all over, Cecchi stood on a grassy slope near the Parkfairfax rental office and tried to sum up what had attracted so many people to the World War II vintage red brick complex.

"Environment . . . and location," he said.