This study will evaluate whether V503 (9vHPV vaccine), is well tolerated in girls and women between 12 and 26 years old who have previously been vaccinated with GARDASIL™. Participants will receive vaccination with 9vHPV vaccine or placebo on Day 1, Month 2, and Month 6 of the Base Study. Participants who receive placebo in the Base Study will be eligible to receive vaccination with 9vHPV vaccine on Day 1, Month 2, and Month 6 of the Extension Study.