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Richie and the guys are at Arnold's and talk about cheerleaders. Ralph tells the guys about a dream where he is a judge in a beauty contest. Richie asks Cynthia, who is a cheerleader, on a date to a drive-in movie but is laughed at. The guys go over to talk to Fonzie at his place. They tell him they are in a dating rut and that neither of them had ever dated a cheerleader. Fonzie tells them they should hold a beauty contest, and offer a trip to Hollywood to the winner. Fonzie tells them they should plant a girl to win that they can trust who won't accept the prize. Richie doesn't like the idea of a plant. In addition to the trip, they offer lunch at the Brown Derby with Efrem Zimbalist Jr. Richie wants to back out of the contest but reconsiders when Cynthia signs up. Richie and Cynthia go out as she tries to persuade him to vote for her. Ralph comes over to the house, and Howard talks to them about the beauty contest. Howard says that if they promise prizes they can't deliver, they're going to be in a lot of trouble. After the talent portion of the conest, Mrs. Elizabeth Bopton, the mailman's wife, plays the piano. Fonzie arrives and tells the guys that the girl he had planned on using as the plant wouldn't be coming. The girls come out in their swimsuits, and the three finalists are announced: Bunny Showalter, Cynthia Miley, and Ann Louise Milligan. Richie suggests asking a question to each girl to decide the winner. They want to pick someone who is most likely not to accept the prizes. They pick Ann Louise Milligan as Miss Arnold's, and Potsie sings "The Most Beautiful Girl in the World." Ann Louise wants the prizes, and the girls go after the guys for declining and staging a fake contest. Fonzie changes the prize to a month of dates with him. At the house, Howard chastizes Richie and asks him if it was worth it, and Richie broadly smiles.

Songs in this episode:
"All I Have To Do Is Dream" by The Everly Brothers (1958)
"Birth of the Blues" by Frank Sinatra (1952) (sung by one of the contestants)
"The Most Beautiful Girl in the World" (1935) (sung by Potsie)