But the testiest part of the exchange came when an audience member suggested that gay people should be allowed to marry because they have a right to happiness.

In response, Mr. Santorum asked whether she thought that more than two people should be allowed to marry, apparently trying to suggest that the questioner was advocating an extreme position.

“If you’re not happy unless you’re married to five other people, is that O.K.?” he asked.

That angered the audience, which booed his answer.

“I’m happy to engage in a discussion,” he continued, saying that he wanted to “give people a chance to answer, but we’re going to have a civil discussion.”

The woman who had asked the first question then persisted, saying that the question about bigamy was “irrelevant.”

“In my personal opinion, go for it,” she said. “But when two men want to marry … ”

Mr. Santorum interrupted, “What about three men?”

“That’s not what I’m talking about,” the woman said to Mr. Santorum, who spent close to an hour and a half before the crowd.

The session ended with many of the students booing Mr. Santorum as he left for his next event.