NEW LONDON, N.H. — Three nursing students have sued a New Hampshire college after they failed a required course that was overbooked.

The students from Maine, Massachusetts and Rhode Island say Colby-Sawyer College needed to “thin the herd” of nursing students, so it failed them.

Colby-Sawyer requires its nursing students to complete a course — usually in the sophomore year — that includes classroom instruction, lab work and a clinical internship. The pass-fail course taught in the spring is limited to 36 students; the lawsuit says 51 students applied for it in 2014.

The college offered the remaining 15 students three options, including a summer course taken by the three who sued. Of the 15 students who took the summer course, 11 failed, were induced to changed majors or left the program. The summer course cost the students $1,800 in tuition plus $100 a week for room and board.

The lawsuit claims the three students — JoAnna Densmore of New Gloucester, Maine; Julia Shriver of Mansfield, Massachusetts; and Kristina Fuccillo of Smithfield, Rhode Island — started off well with a substitute professor who praised their work for three weeks. Then, when the regular instructor returned, the students were held to a higher standard than those students who had completed the coursework in the spring semester, the suit said. The students say they were assessed unfairly compared with other students in the summer program and weren’t given required evaluations or plans to improve performance.

In the lawsuits filed in August in U.S. District courts in the women’s home states, they claim Colby-Sawyer saw that it had too many nursing students heading into the 2015 and 2016 academic years so it orchestrated a plan to reduce the number.

Brad Cook, a lawyer for the private college, says Colby-Sawyer treated the students fairly and went out of its way to help them meet requirements.

The suit claims deceptive business practices and breach of contract. The students want a judge to order Colby-Sawyer to remove the failing grades from their transcripts, award undisclosed damages and pay their legal costs.