The county's fire and rescue service said it was "overwhelmed" with the response and the fact that 150 of the applicants were female.
County area manager, John McVay, said the number would be shortlisted to 100, with nine women guaranteed to go through to the next phase.
But he said no women would be guaranteed a job and the roles would go to the best candidates.
It is the county's first firefighter recruitment drive in eight years.
Shortlisted candidates will face physical fitness, strength and agility tests.
Mr McVay said: "There is perception that a firefighter is predominantly a male role and we are trying to change that.
"We know and understand that the role of a firefighter is for everyone.
"It is also not all about physical strength and fitness. We want people who are disciplined and can take orders, but also people who can go into schools and talk about fire safety."
In the past decade the county has seen a 50% reduction in fire incidents, a spokesman for the fire service said.
More than 1,000 people applied for 15 jobs as a full-time fighter in Cumbria.