The Fairfax Office of Adult and Community Education encourages prospective students to come tonight and, for $1, sample a variety of more than 50 courses offered this fall. By contributing $1 for every course that catches their interest, prospective students can meet the course's instructor and have an introductory first lesson. Subject options include: "New Concepts in Art," "What's New With Taxes?", "Your Child's Self-Esteem," "Quilt in a Day," and "Get It Done! Computer." Dollar Night will start at 7 p.m. and end at 9:30 p.m. at the Bryant Adult and Community Education Center, 2709 Popkins Lane, Alexandria. There will be door prizes.

Applications for homebound voters to register to vote at their residences must be turned in to the general registrar of Virginia at least five days before the anticipated registration day. This fall, the days designated for homebound registration are Sept. 21 and Oct. 1. By appointment only, a voter registrar will visit the home of anyone who has been homebound for at least 30 days because of a long-term illness or physical disability, and who is unable to apply for voter registration in person. Eligible persons of voting age may request an appointment by contacting the office of the general registrar at 558-2345 (voice) or 558-2656 (TDD) between 8 a.m. and 5 p.m. Monday through Friday. Or write: General Registrar, Room 130, Court House, Arlington, Va. 22201.

Open auditions for the Burke Centre Players' fall musical production, "The Fantasticks," will be held at 2 p.m. Saturday and Sunday at Burke Presbyterian Church. "The Fantasticks" requires a cast of six men, at least 17 years old, and one young woman. There is also one nonspeaking role for a person of either sex. Auditioners are expected to perform a song that is not from the show and bring sheet music for the pianist. "The Fantasticks" will be produced Nov. 6 through 8, 13 through 15, and 20 and 21 at The Landings Community Center in Burke Centre. Burke Presbyterian Church is located at 5690 Oak Leather Dr., Burke, Va. For more information, call Gae Schmitt Johnson at 250-7788 or Dave Frydenlund at 278-8823. The 20th century transformation of Arlington from rural community to prosperous urban area will be the topic of discussion at the first bimonthly program meeting of the Arlington Historical Society's 1987-88 season on Friday. A panel of speakers will cite changes that resulted in the development of Arlington's transportation, politics, education and social profile at 8 p.m. to the Arlington Historical Museum, 1805 S. Arlington Ridge Rd. The meeting is free and open to the public. For more information, call 892-4204.

The Alexandria Jaycees urge Alexandria residents and firms to contribute what they can to its auction to raise funds for community projects, to be held at the Ramsey Elementary School between 10 a.m. and 5 p.m. on Saturday. Suggested donations include services, products or simply unwanted household items. Ramsey Elementary School is located at 5700 Sanger Ave., off of North Beauregard Street, Alexandria. For information about the auction or about making a donation, call Dave McEvoy at 820-6470 or Hugo Blankingship at 273-4825.