Additional Study Information: This study is for women with one of the following cancers, cancer of the ovary, fallopian tube or peritoneum and you had previous treatment with carboplatin or cisplatin. The purpose of this research study is to find a different treatment for platinum-resistant TP53-mutated high-grade serous (HGS) ovarian cancer patients. The investigational drug AZD1775 is being combined with standard chemotherapy in subjects with TP53-mutated, advanced ovarian, fallopian tube or peritoneum cancer that no longer responds to platinum therapy. AZD1775 is also being studied in lung cancer and other solid tumors throughout the world. Some ovarian cancer patients have experienced tumor shrinkage while receiving AZD1775 plus chemotherapy. In this study, one chemotherapy drug will be combined with AZD1775 to treat your type of cancer. Three different chemotherapy and AZD1775 schedules will be tested. The combinations to be tested are: Gemcitabine plus AZD1775, Paclitaxel plus AZD1775, and Carboplatin plus AZD1775. Gemcitabine, paclitaxel, and carboplatin are FDA approved to treat patients with previously treated ovarian cancer.