More than 250,000 New Yorkers have completed applications for New York's health insurance exchange, and 76,177 have enrolled since it opened Oct. 1, the state announced Monday.

The state Department of Health said that of the more than 76,000, 41,021 have enrolled in health plans on the exchange and 35,156 have qualified for Medicaid.

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A health department spokesman said the department did not have statistics yet for the number of small businesses that have enrolled for health plans on the exchange.

NY State of Health is the state's online insurance marketplace for individuals or small businesses with 50 or fewer employees as part of the federal Affordable Care Act. The exchange allows consumers to choose from private insurance plans. People must enroll by Dec. 15 for coverage that begins Jan. 1, but have until March 31 to buy insurance for next year.

New York's exchange has had fewer problems than the federal government's marketplace website, which has been beset with computer glitches. In the first month of enrollment, 106,185 were fully processed by health exchanges throughout the country, the federal Department of Health and Human Services said Nov. 13. Most of those were on the 17 state-run exchanges. Only a quarter of the people selected plans through the federally run marketplaces, HHS said.

The state health department said enrollment figures will be updated weekly on the marketplace homepage,