Even when she applied last spring, Delores O. Montgomery did not really think she would win a chance to buy a moderately priced Southeast Washington town house from the city government. That feeling was reinforced on Thanksgiving, when her relatives gently, teasingly, told her she was not a lucky person.

But they were wrong. Last night, Montgomery's name was drawn from a brown paper lunch bag, and she became the representative of one of 24 families who will be able to buy town houses that are part of the city's Linda Arms housing project.

"I'm coming back where my roots are," said Montgomery, who was born in Washington but has lived for the past six years with her two sons, in a suburban Maryland apartment. The three-bedroom town house she now can purchase for $32,500 will be the first home Montgomery, a paralegal specialist at the Federal Trade Commission, has been able to afford, she said.

"Winning has never been for me," Montgomery added, hugging her uncle, Clarence Jackson, her eyes brimming with tears. "I've never been that fortunate. I just don't believe it."

Montgomery was one of 550 persons who applied to the D.C. Department of Housing and Community Development for one of the 24 houses, located in the 3300 and 3400 blocks of C Street SE and the 3300 block of Croffut Place SE. The homes are part of Washington's urban homesteading program, and represent the city's first attempt to include multifamily buildings for single-family homeownership under the program.

Those 550 applicants were narrowed to 60 families who were eligible for the program. Those 60 families selected the town house they wanted to buy, and names were drawn out of paper bags last night to determine which family received a chance to buy each house.

The names were drawn by 4-year-old Belal Gab-Allah. The youngster drew the names of his parents for the town house they had selected.

The families will buy each home for $32,500 a price that includes $16,000 for rehabilitation. The rehabilitation loan is from the city at 3 percent interest. The rest of the mortgage financing will be made at current conventional rates through local savings and loan associations.

The renovation is being done by the D.C. Housing Industry Corp., a coalition of associations representing realtors, builders, bankers, brokers, and savings and loans. Each of the 12 buildings, each two stories with four apartments, will be converted to two three-bedroom town houses.

The city housing department bought the apartments as part of a 65-unit package from the U.S. Department of Housing and Urban Development.

HUD had insured the mortgage on the Linda Arms project, and acquired it when the owner failed to make mortgage payments.

To qualify for a unit, one must not own any other residential property, and must be in a household with at least two persons headed by a person at least 21 years old. Families must agree to live in their new houses at least five years.

Priority is given to families with incomes less than $18,000 a year.

D.C. homesteading is similar to the national homesteading program that HUD administers. That program provides homeownership - often for as little as $1 - and helps revitalize entire blocks.

With last night's 24 winners, the District now has 70 urban homesteading families.