The goal of this clinical trial is to learn about the side effects and effectiveness of this novel four-drug combination of chemotherapy (decitabine, selinexor, carboplatin and paclitaxel) on patients with relapsed ovarian, fallopian or primary peritoneal carcinoma.

Recently the investigators have found that the combination of decitabine and selinexor, two Food and Drug Administration (FDA) approved chemotherapy agents, may prevent or reverse the development of drug resistance and further the remissions and duration of remissions with standard ovarian cancer chemotherapy with carboplatin and paclitaxel. As decitabine and selinexor are not FDA approved for the participant's cancer, these agents are investigational.

Participants enrolled in this study protocol will receive therapy with decitabine followed by usual doses of carboplatin and paclitaxel for one cycle. If the participant tolerates this well, the selinexor will be added to the second and subsequent cycles of therapy given at 4-week intervals, in the out-patient setting. The participant will be asked to complete 9 study visits during their active therapy during each cycle: Days 1-5 of each cycle the participant will receive decitabine treatments over 1 hour, with carboplatin and paclitaxel given on day 6. Paclitaxel alone will continue weekly for 3 weeks on days 13, 20 and 27 of the 28-day cycle. The 5 days of daily decitabine therapy lasts about 1 hour and the carboplatin and paclitaxel treatment last 4 hours, with single agent paclitaxel being only 1 hour.

Selinexor is not added until cycle 2 and is given orally weekly on days 7, 14, 21, and 28 of the 28-day cycle. Weekly clinic visits are required for the first two cycles at the time paclitaxel is administered.

The participant's progress will be assessed and if a remission is achieved the participant would continue the therapy for up to 6 cycles.

Inclusion Criteria:

• Participants must be greater than or equal to 18 years of age
• Participants must have an Eastern Cooperative Oncology Group (ECOG) Performance Status PS less than or equal to 2.
• Participants must have histological or cytological proven epithelial ovarian cancer, fallopian tube or primary peritoneal carcinoma with relapse or disease progression after prior treatment by exam, computed tomography (CT), PET/CT, or magnetic resonance imaging (MRI) may be enrolled. All cell types including clear cell carcinoma are eligible.
• Participants must have failed or relapsed after a platinum and taxane containing combination
• Participants must have adequate hepatic function
• Participants must have adequate renal function
• Participants must be able to swallow and retain oral medications
• Participants must have measurable disease according to Gynecologic Cancer Intergroup CA125 criteria
• Participants with stable (for 2 months or longer), treated (by radiotherapy) CNS metastases are eligible
• Participants with active hepatitis B virus (Hep B) are allowed if antiviral therapy for hepatitis B has been given for greater than 8 weeks.

Exclusion Criteria:

• Participants must not have received Selinexor or another XPO1 inhibitor previously.
• Participants must not have had any concurrent medical condition or disease (eg, uncontrolled active hypertension, uncontrolled active diabetes, active systemic infection, etc.)
• Participants must not have uncontrolled active infection. Participants on prophylactic antibiotics or with a controlled infection within 1 week prior to C1D1 are acceptable.
• Participants must not have known intolerance, hypersensitivity, or contraindication to platinum or taxane therapy
• Participants must not have active, unstable cardiovascular function
• Participants must not have myocardial infarction within 3 months prior to starting
• Participants with untreated central nervous system (CNS) metastases are ineligible.
• Participants must not have had prior chemotherapy or radiation therapy
• Participants must not have DVT related to metastatic disease requiring ongoing anticoagulation.