Parents shut out of their prekindergarten of choice will have a second chance to apply, starting Monday, when 2,000 or so still-available seats will become open for bids.

Although more than 8,800 parents were informed earlier this month that they had not received a slot, that was in part because many of them had put down only one choice, leaving dozens of pre-K programs under-enrolled.

Parents interested in applying for one of the available seats should apply directly to one of these schools, Department of Education officials said.

Zoned students with siblings at the school take top priority. Zoned students without a sibling at the school take second priority.

More information about the city’s prekindergarten program is available on the Department of Education’s Web site.