LOS ANGELES (CBSLA.com)  — Hillary Clinton, the former first lady turned senator turned secretary of state, made even more history Tuesday when she became the first women to win a major party’s nomination as president of the United States.

She is already inspiring a new generation of girls and young women.

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CBS2’s Kristine Lazar shows how Clinton is doing just that.

She spoke to juniors at Notre Dame Academy, an all-girls school. While the students won’t be old enough to vote in November, they are still inspired nonetheless to reach higher.

“It opens a door to me as a person,” says 16-year-old Taylor Orbone. “I have the potential to do just about anything. The president is the most important job in the country.”

“It think it really motivates me that I could actually change the world,” said a classmate.

“It reinforced the idea,” said Boyce Buchanan, “that I can do anything I really want to do.”

In her victory speech Tuesday night, Clinton called her win a milestone.

“There are still ceilings for women to break,” she said, “for all of us, but don’t let anyone tell you that great things can’t happen  America. Barriers can come down.”

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It’s the second such milestone these students have witnessed.

They were in grade school when the country elected Barack Obama, the country’s first black president.

“I definitely feel as a black female more of my dreams are in reach,” said Orbone.

Last night on Facebook, Clinton posted a photo of herself looking down at a young girl who was looking up at her. She added the message: “To every little girl who dreams big, yes, you can be anything you want — even president. Tonight is for you.”

Dan Schnur, director of the Jesse M. Unruh Institute of Politics at USC, said Clinton discussing gender Tuesday evening was fine but talking about her gender will not be in her best interests.

“Hillary Clinton was entitled to her victory lap last night,” Schnur said, “but for the next few months, talking about the historic nature of her victory, is all about her. Much smarter, politically, will be to talk about what it means to the voters and their concerns on an every day basis.”

In fact, Schnur said many college-age women aren’t necessarily Clinton supporters, simply because she’s a woman, unlike some of the older generation.

“One of Clinton’s real challenges in this campaign,” he said, “has been trying to explain to young female voters, why the accomplishments of the feminists of her generation, should be relevant to their lives.”

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Women are still largely underrepresented in Congress. Though more than half the population, women only make up about 20 percent of the House and Senate.