The Arlington School Board, faced with complaints about the difficulty of enrolling children in the county's popular alternative schools, decided last night to select students for one of the three schools in the program through a lottery.

Admission to the other two alternative schools will continue to be on a first-come, first-served basis.

The random selection process through a lottery will be used to choose new students for the Page Traditional School, starting in the fall of 1991. The lottery is to be used on a trial basis for two years.

Students at the other two alternative schools -- Drew Model Elementary and H-B Woodlawn, which has grades 6 through 12 -- will continue to be admitted on a first-come basis. Drew and Woodlawn stress flexible class structuring and students are given greater initiative than at the county's other schools.

The lottery for Page admissions will be held next December. The change was agreed to on a 3 to 2 vote after an hour's debate and several inconclusive votes.

Brothers and sisters of students already enrolled at Page are to be automatically admitted under the new policy. Minority applicants at all three alternative schools will continue to be given preference.

Board members said they had gotten numerous phone calls and letters from parents opposing the changes proposed in the enrollment procedure in the two months since they were recommended by Superintendent Arthur W. Gosling.

"So what if parents are lined up," said Joyce Williams, a parent of two pre-school children whom she plans to enroll in the Drew program. "If you want the best for your child and it means standing out all night, then that's what you do. That's what being a parent means."

Ray Anderson, principal at H-B Woodlawn, was also opposed to changes at his school. "I think the decision ought to be based on finding the most appropriate students for the school. The parents who make the effort to get there early are the parents who feel strongly enough about it that they would stand in line."

Gosling argued that admissions changes were necessary at all three schools to create a more equitable system and to eliminate lines that have grown more and more unwieldy each school year. At each of the schools, and especially at Page, parents have queued up at times days in advance of the registration date under the first-come, first-served system.

"I think the next task is for us to go back and review the current policy," Gosling said after the vote.

"It was obviously a very, very difficult issue for the board and dealt with issues of equity, parental concerns and keeping families together. These are not right or wrong kind of issues. They represent a series of values choices that the board was grappling with," Gosling said.

Voting for the new lottery system at Page were Gail Nuckols, Frank Wilson and Steven Ivins; voting against were Conchita Mitchell and Dorothy Clark.