Her hair isn't yet platinum and her makeup is still more girlish than glamorous, but Lana Turner is nonetheless a walking acetylene torch in her first top billing, playing a dancer planted in a big Midwest college to win a rigged Hollywood contest. The prize: the starring role in a big movie musical. The complications: plenty, especially when the co-ed falls for a crusading college newshound (Richard Carlson) who suspects the contest is as phony as a press agent's smile. But the real romance happened the next year when Dancing Co-Ed co-star Artie Shaw - whose swing music is as white-hot as the leading lady's starpower - took Turner out on their first date. They came back the next day from Las Vegas.married.