NEW YORK — ‘‘That’s right, one lucky woman will win the ultimate chance at starting or building her family,’’ said a contest announcement issued in April by Long Island IVF, a clinic in Melville, N.Y., that offers in vitro fertilization to women who are having difficulty conceiving.

Contestants were asked to submit ‘‘the most emotional or entertaining essays and homemade amateur videos’’ explaining why they wanted a free round of in vitro fertilization.