Selective Inhibitor of Nuclear Export, Selinexor (KPT-330) in Combination With Paclitaxel and Carboplatin in Patients With Advanced Ovarian or Endometrial Cancers

Inclusion Criteria: * Patients must have MSKCC pathologically confirmed diagnosis of one of the following tumor types: Ovarian, fallopian tube or primary peritoneal cancer, Ovarian carcinosarcoma, Endometrial cancer, Endometrial carcinosarcoma * All patients with ovarian, fallopian tube or primary peritoneal cancer and ovarian carcinosarcoma must have recurrent disease, and only one prior line of chemotherapy that must have been platinum-based chemotherapy for the management of primary disease. This initial platinum-based treatment may have included intraperitoneal therapy, consolidation/maintenance and/or biologic/targeted agents (e.g., bevacizumab, PARP inhibitor) as part of first-line treatment. * Patients with endometrial cancer or endometrial carcinosarcoma may either be chemotherapy naive OR have had one prior line of chemotherapy that must have been a platinum-based chemotherapy regimen in the adjuvant or advanced/recurrent setting. The initial platinum-based treatment may have included consolidation/maintenance and/or biologic/targeted agents as part of first-line treatment. Patients entering the trial chemotherapy naive MUST have Stage IVB or recurrent disease AND have disease that is not amenable to curative intent. * Patients must have measurable disease (RECIST 1.1). Measurable disease is defined as at least one lesion that can be accurately measured in at least one dimension (longest diameter to be recorded). Each lesion must be greater than or equal to 10 mm when measured by CT, MRI or caliper measurement by clinical exam; or greater than or equal to 20 mm when measured by chest x-ray. Lymph nodes must be greater than or equal to 15 mm in short axis when measured by CT or MRI. * Tumors within a previously irradiated field will be designated as "non-target" lesions unless progression is documented or a biopsy is obtained to confirm persistence at least 90 days following completion of radiation therapy. * Be at least 18 years of age. * Have an Eastern Cooperative Oncology Group (ECOG) performance status of 0-1. * Have adequate bone marrow, renal, hepatic and neurologic functions as defined by the following: Bone marrow function: * Absolute neutrophil count (ANC) ≥ 1.5 x 109/L * Platelets ≥ 100 x 109/L * Hemoglobin ≥ 9 g/dL Renal function: * Creatinine ≤ 1.5 x ULN OR creatinine clearance ≥ 30 mL/min (Cockcroft-Gault calculation) Hepatic function: * Bilirubin ≤ 1.5 x ULN * AST and ALT ≤ 3 x ULN (less than or equal to 5 x upper limit of normal for patients with liver involvement of their cancer) (ULN = institutional/laboratory upper limit of normal; LLN = institutional/laboratory lower limit of normal) * Neurologic function: Neuropathy (sensory and motor) less than or equal to Grade 1. * Patients must have recovered from effects of recent surgery, radiotherapy, chemotherapy or biologic/targeted therapy to baseline or CTCAE less than or equal to Grade 1 (excluding alopecia or other non-clinically significant AE's). * Any hormonal therapy directed at the malignant tumor must be discontinued at least one week prior to study treatment initiation. * Any other prior therapy directed at the malignant tumor, including chemotherapy, biologic/targeted therapy and immunologic therapy, must be discontinued at least 3 weeks prior to study treatment initiation. * Any investigation agents must be discontinued at least 30 days prior to study treatment initiation. * Any prior radiation therapy must be discontinued at least 4 weeks prior to study treatment initiation. * At least 4 weeks must have lapsed since major surgery (e.g., laparotomy, laparoscopy, thoracotomy, video assisted thoracoscopy) prior to study treatment initiation. * Patients must be willing and able to swallow oral tablets. * Patients must have signed an approved informed consent and authorization permitting the release of personal health information. * Patients of childbearing potential must have a negative pregnancy test prior to the study entry and be practicing an effective form of contraception. Sexually active subjects must agree to use medically accepted barrier methods of contraception (e.g., male or female condom) during the course of the study and for 4 months after the last dose of study drug, even if oral contraceptives are also used. All subjects of reproductive potential must agree to use both a barrier method and a second method of birth control during the course of the study and for 4 months after the last dose of study drug. Pregnant women are excluded from this study because of the potential for teratogenic or abortifacient effects. Exclusion Criteria: * Patients who are pregnant or nursing. * Patient who have had previous treatment with selinexor. * Patients with history or evidence upon physical examination of CNS disease, including primary brain tumor, seizures which are not controlled, any brain metastases and/or epidural disease, or history of cerebrovascular accident (CVA, stroke) within six months prior to the first date of study treatment. * Patients requiring drainage gastrostomy (e.g., drainage PEG tube) and/or parenteral hydration and/or nutrition. * Patients with clinically significant cardiovascular disease. This includes: * Uncontrolled hypertension, defined as systolic greater than or equal to 160 mm Hg or diastolic greater than or equal to 100mm Hg despite antihypertensive medications. * Myocardial infarction or unstable angina within 6 months prior to the first date of study treatment. * New York Heart Association (NYHA) Class II or greater congestive heart failure. * History of serious ventricular arrhythmia (i.e., ventricular tachycardia or ventricular fibrillation) or serious cardiac arrhythmia requiring medication. This does not include asymptomatic atrial fibrillation with controlled ventricular rate. * Corrected QT interval calculated by the Fridericia formula (QTcF) \> 500 ms. Note: if initial QTcF is found to be \>500 ms, two additional ECG's separated by at least 3 minutes should be performed. If the average of these three consecutive results for QTcF is less than or equal to 500 ms, the subject meets eligibility in this regard. * Any life-threatening illness, medical condition or organ system dysfunction which, in the investigator's opinion, could compromise the subject's safety, or put the study outcomes at undue risk * Uncontrolled active infection requiring parenteral antibiotics, antivirals, or antifungals within one week prior to the first date of study treatment. * Patients with macular degeneration, uncontrolled glaucoma, or markedly decreased visual acuity